System for generating an anamorphic image from a non-anamorphic image

ABSTRACT

A system for displaying an anamorphic image on a viewing surface comprises a screen having a viewing surface and an image source configured to display the anamorphic image on the viewing surface such that an image viewed on the viewing surface appears undistorted from a viewing point. In addition, the system may also include a reflective lens having a convex exterior surface and a refractive lens having a plurality of surfaces to redirect light toward an image capture device. Further, the system may include an image conversion module for converting a non-anamorphic image into the anamorphic image suitable for displaying on the viewing surface and a selected portion of the anamorphic image into at least one non-anamorphic image.

RELATED APPLICATIONS

This application is a division of U.S. patent application Ser. No.15/232,218, filed Aug. 9, 2016, now U.S. Pat. No. 9,690,081, which is acontinuation of U.S. patent application Ser. No. 14/223,720, filed Mar.24, 2014, now U.S. Pat. No. 9,411,078, which is a division of U.S.patent application Ser. No. 12/671,867, filed Feb. 2, 2010, now U.S.Pat. No. 8,678,598, which is a 371 of International Application No.PCT/US08/72719, filed Aug. 8, 2008, which claims benefit under 35 U.S.C.§119(e) of U.S. Provisional Patent Application No. 60/954,627, filedAug. 8, 2007, and U.S. Provisional Patent Application No. 60/954,636,filed Aug. 8, 2007, both of which are hereby incorporated by referencein their entireties.

TECHNICAL FIELD

This disclosure relates to devices and methods for capturing,manipulating, and displaying an image having a wide (e.g., panoramic 360degree) field of view.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-section of a refractive lens according to oneembodiment.

FIG. 2 is an enlarged cross-section of the refractive lens of FIG. 1.

FIG. 3 is an enlarged cross-section of the refractive lens of FIG. 2illustrating a ray intersecting an outer surface of the refractive lensat a 90 degree angle of incidence.

FIG. 4 is an enlarged cross-section of the refractive lens of FIG. 2illustrating the refraction of the ray of FIG. 3 as it travels from thelens media (e.g., glass) to an internal media (e.g., air).

FIG. 5 is an enlarged cross-section of the refractive lens of FIG. 2illustrating the refraction of the ray of FIG. 4 as it travels from theinternal media to the lens media.

FIG. 6A is an enlarged cross-section of the refractive lens of FIG. 2illustrating the refraction of the ray of FIG. 5 as it travels from thelens media to an external media (e.g., air).

FIG. 6B illustrates the extent to which a ray segment refracts afterpassing through the refractive lens of FIG. 2.

FIG. 7 is a cross-section of a reflective lens according to oneembodiment.

FIG. 8 is an enlarged cross-section of the reflective lens of FIG. 7.

FIG. 9 is an enlarged cross-section of the reflective lens of FIG. 7illustrating a ray reflecting off an outer surface of the reflectivelens.

FIG. 10A is a perspective view of a display according to one embodiment.

FIG. 10B is a cross-section of the display of FIG. 10A.

FIG. 11A illustrates an example of an image that might be captured usingthe refractive lens of FIG. 1 or reflective lens of FIG. 7.

FIG. 11B illustrates an example of an image that might captured using afisheye lens.

FIG. 12A is a graphical representation of converting images capturedwithout using the refractive lens of FIG. 1 or reflective lens of FIG. 7(e.g., an image captured using a traditional camera) to a formatsuitable for viewing on the display of FIG. 10A, according to oneembodiment.

FIG. 12B is a flowchart illustrating a method of converting imagescaptured without using the refractive lens of FIG. 1 or reflective lensof FIG. 7 (e.g., an image captured using a traditional camera) to aformat suitable for viewing on the display of FIG. 10, according to oneembodiment.

FIG. 13 illustrates an example of converting an image captured using atraditional camera to a format suitable for viewing on the display ofFIG. 10A.

FIG. 14 illustrates an example of converting a traditional graphicaluser interface display for a computer to a format suitable for viewingon the display of FIG. 10A.

FIG. 15 illustrates an example of converting an image suitable forviewing on the display of FIG. 10A to a format suitable for printing asa photograph having a traditional aspect ratio.

FIG. 16 is a perspective view of a station display (e.g., computer orworkstation display) according to one embodiment.

FIG. 17 is a perspective view of a room display (e.g., home theater orconference room) according to one embodiment.

FIG. 18 is a perspective view of a theater display (e.g., movie theater)according to one embodiment.

FIG. 19 is a perspective view of a camera utilizing the refractive lensof FIG. 1.

FIG. 20 is a block diagram showing operational components of the cameraof FIG. 19, according to one embodiment.

FIG. 21 is a block diagram showing operational components of an examplecomputer.

DETAILED DESCRIPTION OF EMBODIMENTS

With reference to the above-listed drawings, this section describesparticular embodiments and their detailed construction and operation.The embodiments described herein are set forth by way of illustrationonly. In light of the teachings herein, those skilled in the art willrecognize that there may be equivalents to what is expressly orinherently taught herein. For example, variations can be made to theembodiments described herein and other embodiments are possible. It isnot always practical to exhaustively catalog all possible embodimentsand all possible variations of the described embodiments.

For the sake of clarity and conciseness, certain aspects of componentsor steps of certain embodiments are presented without undue detail wheresuch detail would be apparent to those skilled in the art in light ofthe teachings herein and/or where such detail would obfuscate anunderstanding of more pertinent aspects of the embodiments.

As one skilled in the art will appreciate in view of the teachingsherein, certain embodiments may be capable of achieving certainadvantages, including by way of example and not limitation one or moreof the following: (1) providing improved image capture; (2) providingimproved display of panoramic images; (3) providing a display thatsurrounds and immerses a user in an image; (4) providing a lens shapedto capture a panoramic 360 degree field of view; (5) providing a displayto view the panoramic 360 degree field of view; (6) generating anundistorted image that has a uniform image density when viewed; (7)providing a projection system that provides a user with an unobstructedview of an image; (8) providing a single camera for image capture; (9)providing a lens having no moving parts; (10) providing an imagecollection and viewing system that immerses the viewer in the image byproviding a horizontal field of view of 360 degrees and vertical fieldof view approximately 240 degrees measured from the furthest extent ofthe viewing surface across the azimuth, directly above the viewer, andextending to the opposite furthest extent of the viewing surface; (11)providing an imaging system having a large field of view; (12) providinga lens that can be retrofitted onto a standard camera; (13) capturingimages having a large field of view without stitching a combination ofimages together; and (14) providing a system that accommodates thecapture, creation and image manipulation by algorithms and the displayof still or motion images. These and other advantages of variousembodiments will be apparent upon reading the following.

According to one embodiment, an immersion vision imaging systemcomprises one or more lenses, viewing surfaces, and algorithms toimmerse a viewer in an image—i.e., give the viewer a panoramic field ofview of the image spanning up to 360 azimuth degrees and approximately120 zenith degrees. To capture a wide-angle still or motion image, acamera may be retrofitted with a lens as described in more detail below.In addition, one or more algorithms may be used to convert imagescaptured without using the lenses described below (e.g., an imagecaptured using a traditional camera) or a graphical user interface to aformat suitable for viewing on a specially designed screen. The capturedand/or converted images can then be projected onto the speciallydesigned screen to immerse the viewer in the image. Images from multiplesources (e.g., an image captured using a camera having a lens asdescribed below and an image converted using one or more of thealgorithms described below) can be concurrently displayed on thespecially designed screen. Thus, an image of a movie having atraditional aspect ratio, such as Gone with the Wind, can be displayedwithin an image having a nontraditional aspect ratio, such as an imageof the temple of Amen-Ra in Egypt, surrounding the viewer. Additionally,the displayed images can be cropped and converted to a format having atraditional aspect ratio. Thus, a user can select all or a portion of adisplayed image and print the image with a traditional printer.

Image Capture

By way of example, traditional cameras have a horizontal field of viewof about 40 degrees and a vertical field of view of about 30 degrees.Retrofitting the same camera with one of the lens described belowprovides a 360 degree horizontal field of view (i.e., 360 azimuthdegrees) and an approximately 240 degree vertical field of view (i.e.,120 zenith degrees as measured from the positive z-axis to the furthestextent of the vertical field of view). As used herein, the azimuthalangle, θ, refers to an angle in the xz-plane from the positive y-axis(i.e., the angle between the positive y-axis and a line formed betweenthe origin (the intersection of the x-axis, y-axis, and z-axis) and aprojection of a three-dimensional point onto the xz-plane) and the polarangle, expressed in zenith degrees φ, refers to the angle between thepositive x-axis and a line formed between the origin and thethree-dimensional point. The azimuthal angle is typically within therange of 0≦θ≦2π radians (0°≦θ≦360°) and the polar angle is typicallywithin the range of 0≦φ≦π radians (0°≦θ≦180°). The lens may berefractive or reflective, each of which will be described in more detailwith reference to FIGS. 1 through 6 and FIGS. 7 through 9, respectively.

Refractive Lenses

Referring now to FIG. 1, a cross-sectional view of a refractive lens isprovided. According to one embodiment, the non-spherical refractive lenshas a hollow interior. The lens may be constructed from two parts (e.g.,lens 1 and lens 2), such as glass or plastic, which may be the same ordifferent materials. The two-piece construction aids in the constructionof the lens. For example, lens 1 can be formed by injecting an opticallyclear medium, such as glass or plastic, into a void between interior andexterior forms and lens 2 can be formed in a similar manner without theuse of the interior form. In addition, the non-spherical refractive lensmay be constructed in other ways, such as layer-by-layer usingstereolithography, or a similar process. The overall dimensions of thelens varies based on the application.

All light headed to a station point SP enters a outermost surface of thelens. The light heading towards the station point SP refracts throughsubsequent lenses to converge at a camera point CP2. As the light raystravel to a camera point CP2, they pass through an imaginary pictureplane IPP having a curved surface. In one embodiment, the imaginarypicture plane IPP defines a shape referred to herein as a “Harris”shape. For example, if an impulse of light is directed toward lens 1 attime t=0, the imaginary picture plane IPP defines the location of lightrays originally heading toward the station point SP at some later pointin time, t>0, after having traveled though lenses 1 and 2. In otherwords, as shown in FIG. 1 the light ray represented by the arrow −30degrees below the x-axis travels through more of the medium of lenses 1and 2 than the light ray represented by the arrow 90 degrees above thex-axis. Because the speed of light is slower when traveling throughlenses 1 and 2 (e.g., light travels through glass slower than lighttraveling through a vacuum—approximately 0.6667c) as compared to air(e.g., light travels through air slightly slower than light travelingthrough a vacuum—approximately 0.9997c), it will take longer for thelight impulse traveling along light ray −30 to reach the imaginarypicture plane IPP than the light impulse traveling along light ray 90.

A two dimensional flat image may be captured by an image capture deviceas the light rays converge on a focal plane or viewing plane VP2.According to one embodiment, the viewing plane VP2 is orthogonal to they-axis. As shown, the viewing plane VP2 is located such that the camerapoint CP2 is between the station point SP and the viewing plane VP2.Thus, the image captured at the viewing plane VP2 is inverted (similarto the image captured using the reflective lens described with referenceto FIGS. 7 through 9, except without capturing the camera and camerasupport). If the viewing plane VP2 is located between the camera pointCP2 and the station point SP, the image would not be inverted.

The image capture device may comprise photographic film, film stock, adevice capable of converting electromagnetic waves into an electricalsignal (e.g., a camera having a CMOS or CCD imager), or another devicecapable of capturing an optical image, and may be configured to capturestill or moving images. The resolution of the image capture devicevaries based on the application. For example, in order to capture anddisplay an image having the same image density as a traditional1680×1200 pixel computer screen at an eighteen inch distance, theresolution of the image capture device would increase approximately by afactor of twenty-five, or from approximately two megapixels toapproximately fifty megapixels. Thus, if this ratio holds true fordigital photographic images, a standard ten megapixel photograph mayrequire an image capture device having a 250 megapixel resolution tocapture and display an image having the same image density.

FIG. 1 illustrates light rays traveling to the viewer or the stationpoint SP and are depicted by arrows distributed in 10 degree incrementsfrom −30 degrees to 90 degrees about the station point SP. As the lightrays enter the refractive surface PS1 of the lens 1 they do not refractbecause the surface PS1 is normal, or 90 degrees, to the station pointSP. As the light rays exit the refractive surface PS2 of the lens 1 theybend in the direction of the camera point CP2. As the light rays enterthe refractive surface PS3 of the lens 2 they bend further in thedirection of the camera point CP2. Finally, as the light rays exit therefractive surface PS4 of the lens 2 they bend again and converge on thecamera point CP2.

According to one embodiment, the outside surface PS1 defines a portionof a sphere of refractive material, such as glass, having its center atthe station point SP. Using a semispherical surface for the surface PS1helps ensure that there is no refraction of the light heading toward thecenter point as it enters the surface PS1. The three other surfaces PS2,PS3, and PS4 each play a role in refracting the light rays and shiftingthe focal point so that the final focal point is coincident with thecamera point CP2. Thus, the surface PS1 need not be semispherical if oneor more of the other surfaces PS2, PS3, and PS4 is adjusted tocompensate for the difference. For example, if the surface PS1 isslightly adjusted to shift the focal point from the station point SP toanother point (perhaps closer to CP2), one or more of the other surfacesPS2, PS3, and PS4 could be changed to ensure the final focal point iscoincident with the camera point CP2.

Referring now to FIG. 2, the light rays that were originally headedtoward the station point SP are shown refracting through the variouslens surfaces to result in the light rays converging on the camera pointCP2. The ray segments R1 through R5 (hereafter referred to as simply“rays” for ease of reference) refer to each individual segment of thelight ray as it travels through different media, and the degreesindicates the degrees from the x-axis about the station point SP. Forexample, the rays R1 are those light ray segments that are initiallyheaded to the station point SP and encounter the surface PS1. The raysR2 are those light ray segments that have entered the optical media ofthe lens 1 through the surface PS1 but have not exited the lens 1through the surface PS2. The rays R3 are those light ray segments thathave exited the surface PS2 but have not yet entered the surface PS3 oflens 2. The rays R4 are those light ray segments that have entered theoptical media of the lens 2 but have not exited the lens 2 through thesurface PS4. The rays R5 are those light ray segments that have exitedthe surface PS4 and are traveling to the camera point CP2. As shown inFIG. 2, the portion of lens 2 between the intersection of ray segmentsR4(-30) and R5(-30) extends in a straight line to the bottommost portionof lens 1. However, the portion of lens 2 between the intersection ofray segments R4(-30) and R5(-30) may take another shape, such asextending downward parallel to the y-axis.

FIG. 3 is an enlarged cross-section of the lens of FIG. 2 showing theray segment R1 intersecting the surface PS1 at a right angle. The raysegment R1(-30) is headed to the station point SP at 30 degrees belowwhere the x-axis intersects with the surface PS1. The ray segmentR1(-30) illustrates a light ray, in the air, prior to intersecting thesurface PS1. The ray segment R2(-30) illustrates the light ray, in lens1, after it intersects the surface PS1. The refraction of ray segmentR1(-30) as it passes from one media, such as air having a refractiveindex of n₁=1.0, to a different media, such as glass or a polycarbonatehaving a refractive index n₂=1.51, can be determined from Equation 1(Snell's law), where LNA is the angle of incidence measured from thenormal line N and RNA is the angle of refraction measured from thenormal line N.

n ₁*sin(LNA)=n ₂*sin(RNA)   Equation 1

According to one embodiment, the surface PS1 of lens 1 is semisphericalabout the station point SP. Thus, the ray segment R1(-30) is parallel tothe normal line N (e.g., LNA=0), and there is no refraction as the raysegment R1(-30) intersects the surface PS1 (e.g., RNA=0). As shown inFIG. 3, the horizontal line H is parallel to the x-axis (FIG. 1). Thus,the angle LHA between the ray segment R1(-30) and the horizontal line Hequals 30 degrees (e.g., 30 degrees below the horizontal line H).

FIG. 4 is an enlarged cross-section of the lens of FIG. 2 showing theray segment R2(-30) intersecting the surface PS2. As previouslydiscussed, the ray segment R2(-30) indicates a ray of light travelinginside of the lens 1 prior to intersecting the surface PS2. The raysegment R3(-30) designates the ray of light in the air after theintersection at the surface PS2. The normal line N is perpendicular tothe surface PS2. The tangent line T is tangent to the surface PS2 atpoint PS2(-30) (e.g., the intersection of the ray segments R2(-30) andR3(-30)). The refraction of ray segment R2(-30) as it passes from onemedia, such as glass or a polycarbonate having a refractive indexn₁=1.51, to a different media, such as air having a refractive index ofn₂=1.0, can be determined from Equation 1 above, where LNA is the angleof incidence measured from the normal line N and RNA is the angle ofrefraction measured from the normal line N. An angle LHA is the anglebetween the ray segment R2(-30) to the horizontal line H. An angle THAis the angle between the tangent line T to the horizontal line H. Anangle RHA is the angle between the ray segment R3(-30) to the horizontalline H.

FIG. 5 is an enlarged cross-section of the lens of FIG. 2 showing theray segment R3(-30) intersecting the surface PS3. The ray segmentR3(-30) indicates a ray of light, in the air, prior to intersection ofthe surface PS3 and the ray segment R4(-30) designates the ray of light,in the lens 2, after the intersection at the surface PS3. The normalline N is perpendicular to the surface PS3. The tangent line T istangent to the surface PS3 at point PS3(-30) (e.g., the intersection ofthe ray segments R3(-30) and R4(-30)). The refraction of ray segmentR3(-30) as it passes from one media, such as air having a refractiveindex of n₁=1.0, to a different media, such as glass or a polycarbonatehaving a refractive index n₂=1.51, can be determined from Equation 1,where LNA is the angle of incidence measured from the normal line N andRNA is the angle of refraction measured from the normal line N. Theangle from the ray segment R3(-30) to the horizontal line H is angleLHA. The angle from the ray segment R4(-30) to the horizontal line H isangle RHA. The angle from the tangent line T to the horizontal line H isangle THA.

FIG. 6A is an enlarged cross-section of the lens of FIG. 2 showing theray segment R4(-30) intersecting the surface PS4. The ray segmentR4(-30) indicates a ray of light in the lens 2, prior to intersection ofthe surface PS4 and the ray segment R5(-30) designates the ray of lightin the air after the intersection at the surface PS4. The normal line Nis perpendicular to the surface PS4. The tangent line T is tangent tothe surface PS4 at point PS4(-30) (e.g., the intersection of the raysegments R4(-30) and R5(-30)). The refraction of ray segment R4(-30) asit passes from one media, such as glass or a polycarbonate having arefractive index n₁=1.51, to a different media, such as air having arefractive index of n₂=1.0, can be determined from Equation 1 above,where LNA is the angle of incidence measured from the normal line N andRNA is the angle of refraction measured from the normal line N. Theangle from the ray segment R4(-30) to the horizontal line H is LHA. Theangle from the ray segment R5(-30) to the horizontal line H is RHA. Theangle from the tangent line T to the horizontal line H is THA. The anglefrom the ray segment R4(-30) to the horizontal line H is RHA.

Thus, as illustrated in FIGS. 1 through 6A, the ray of light at the edgeof the field of view (e.g., the ray segment R1(-30)), travels throughthe four refractive interfaces of the lenses 1 and 2. FIG. 6Billustrates the extent to which the ray segment R1(-30) refracts afterpassing through the lenses 1 and 2 and emerges as ray segment R5(-30).The angle between the y-axis and the ray segment R1(-30) isapproximately one-half of the field of view measured from station pointSP, or 120 degrees in the embodiment illustrated in FIG. 6B. The anglebetween the y-axis and the ray segment R5(-30) is φ degrees measuredfrom the camera point CP2. Thus, the ray segment R1(-30) refracts atotal of one-half of the field of view minus φ, or 120 degrees minus φdegrees in the embodiment illustrated in FIG. 6B. While there may beadditional or fewer refraction interfaces, the light ray at the edge ofthe field of view still refracts a total of one-half of the field ofview minus φ (e.g., 120 degrees minus φ degrees) measured from thestation point SP as the ray passes through the multiple refractiveinterfaces.

According to one embodiment, points on the surfaces PS1, PS2, PS3, andPS4 can be determined by first establishing the path of a light ray atthe edge of the field of view as it passes through lenses 1 and 2 andconverges at the camera point CP2, and then by establishing the paths ofthe other light rays within the field of view emanating outward from thecamera point CP2. The ray segment R1(-30) passing through the lens 1 and2 at the edge of the field of view is chosen because it has the largestchange of direction of any of the light rays entering into the lens 1originally headed to the station point SP and refracted to the camerapoint CP2. The light ray traveling along the ray segments R1(-30)through R5(-30) enters and exits the various refractive interfaces andultimately arrives at the camera point CP2. According to one embodiment,the angle φ between the y-axis and the ray segment R5(-30) measured fromthe camera point CP2 (FIG. 6B) is identical to the angle RVA between thevertical line V and ray segment R2(-30) measured from the point PH(-30)on the reflective lens (FIG. 9). According to one embodiment, the angleof total internal refraction is not exceeded for each of the refractivesurfaces of the lenses.

An example of determining points on the surfaces PS1, PS2, PS3, and PS4will be provided with reference to FIG. 1. First, points on the surfacesPS1, PS2, PS3, and PS4 can determined at the edge of the field of viewby tracing the ray segment R1(-30) as it travels through the refractivemedia and emerges as ray segment R5(-30) headed to camera point CP2. Theexample assumes that the station point SP is coincident the origin ofthe coordinate system (e.g., (X,Y,Z)=(0,0,0)), the camera point CP1 hascoordinates (0, 7.2679,0), point e has coordinates (3,−1.7321,0), basepoint BP has coordinates (0,−1.7321,0), D is equal to 120 degrees,ΔF_(RVA) is equal to 1 degree, RVA_(e) is equal to 18.4350 degrees, n1for air equals 1.00029 and n2 equals 1.52 for the refractive lens media.

As illustrated in FIG. 3, there is no refraction when the ray segmentR1(-30) enters the surface PS1 because the light ray is normal to thesurface (e.g., the angle LNA is zero degrees). In this example theintersection of the ray segment R1(-30) and the surface PS1 hascoordinates (9.1812,−5.3007,0). The ray segment R1(-30) enters thesurface of PS1 at −30° from the x-axis (e.g., LHA=−30°) and exits thesurface PS1 at 30° from the x-axis (e.g., RHA=30°).

As illustrated in FIG. 4, as the ray segment R2(-30) passes through thesurface PS2 and emerges as ray segment R3(-30), it refracts away fromthe normal line of the lens surface PS2. In this example theintersection of ray segment R2(-30) and the surface PS2 occurs at pointe having coordinates (3.0000,−1.7321,0). The ray segment R2(-30)approaches the surface PS2 at −30° from the x-axis (e.g., LHA=−30°) andthe angle LNA equals 40.49°. The angle RNA can be determined bysubstituting the known values into Equation 1 (Snell's Law) and solvingfor RNA. Thus, the angle RNA equals 80.64°(1.52*sin(40.49°)=1.00029*sin(RNA)). The ray segment R3(-30) is leavingthe surface PS2 at 10.15° degrees below the x-axis (e.g., RHA=−10.15°).

As illustrated in FIG. 5, as the ray segment R3(-30) passes through thesurface PS3 and emerges as ray segment R4(-30), it refracts away fromthe normal line of the lens surface PS3. In this example theintersection of ray segment R3(-30) and surface PS3 occurs at pointhaving coordinates (2.7051,−1.7849,0). The ray segment R3(-30)approaches the surface PS3 of the lens 2 at 10.15° from the x-axis(e.g., LHA=10.15°) and the angle LNA equals 87.06°. Substituting theknown values into Equation 1 and solving for RNA yields 41.09°(1.00029*sin(87.06)=1.52*sin(RNA)). The resulting ray segment R4(-30)exiting the surface PS3 and heading towards the surface PS4 is 56.12°below the x-axis (e.g., RHA=−56.12°).

As illustrated in FIG. 6A, as the ray segment R4(-30) passes through thesurface PS4 and emerges as ray segment R5(-30), it refracts away fromthe normal line of the lens surface PS4. In this example theintersection of ray segment R4(-30) and PS4 occurs at a point havingcoordinates (1.4674,−3.6280,0). The ray segment R4(-30) approaches thesurface PS4 at 56.12° from the x-axis (e.g., LHA=56.12°) and the angleLNA equals 25.61°. Substituting the known values into Equation 1 andsolving for RNA yields 41.05° 1.52*sin(56.12)=1.00029*sin(RNA). Theresulting ray segment R5(-30) exits the surface PS4 at 71.57° degreesbelow the x-axis (e.g., RHA=−71.57°). The angle RVA_(e)=RHA−90°=18.436°.With reference to FIG. 2, the intersection of the ray segment R5(-30)with the y-axis (e.g., the camera point CP2) can be determined to havecoordinates (0,−8.0302,0) using geometry.

After having established the location of the camera point CP2 andknowing that the angle RVA_(e) is fixed and D equals 120, the shapes ofthe surfaces PS1, PS2, PS3 and PS4 can be determined according to thisexample by extending 120 ray segments R5 outwardly from the camera pointCP2 such that the ray segments R5 are equally spaced between the edgesof the field of view. The number of light rays used to calculate pointson the surfaces can determine the level of precession for the refractivelens surfaces. In this example there is one light ray traced for every 1degree of the field of view about the station point SP, or D=120 for onehalf of the field of view.

In this example, the surface PS4 takes the Harris shape (see, e.g.,Equation 22). Point e is located at the edge of the field of view on thesurface PS2 and was previously calculated to have coordinates(3,−1.7321,0). Because shape of the surface PS4 is known and the angulardirections of all of the ray segments R5 are known, the direction of theray segments R4 can be determined using Equation 1 as previouslydescribed.

The surface of PS3 is initially roughly determined as an arc locatedbetween the surface PS4 and the station point SP. The roughdetermination of the surface PS4 can be accomplished by extending an arcfrom the point of intersection of the ray segment R4(-30) and thesurface PS3 (previously calculated) to the y-axis. The origin of the arcis approximately at the intersection of the surface PS1 and the y-axis.The rough or approximate surface of PS3 is divided into equal segmentscorresponding to the number of light rays analyzed within the field ofview (e.g., 120 in this example). Having determined the approximatesurface of PS3 and knowing the direction of the ray segments R4, thepaths of all the ray segments R3 approaching the surface PS3 can bedetermined using Equation 1.

In this example the point e on the surface PS2 was previously determinedto have coordinates (3,−1.7321,0). Because the normal line to thesurface at point e was previously determined with respect to FIG. 4, thetangent line, which is perpendicular to the normal line, can bedetermined. By extending the tangent line of the surface at point e tointersect with the ray segment R3(-29), the surface PS2 can be definedusing Equation 1 as a surface required to refract the ray segmentR3(-29) to intersect the previously defined location of the intersectionof the ray segment R4(-29) and the surface PS3. Next, by extending thetangent line from the surface at the previously defined point ofintersection of the ray segment R4(-30) and the surface PS3 to intersectwith the ray segment R4(-29) a final location of the surface PS3 at theintersection of the ray segment R4(-29) can be determined.

Next, the tangent line of the surface PS2 at the intersection with theray segment R2(-29) is extended to intersect with the ray rays segmentR3(-28), and the surface PS2 is defined using Equation 1 as the surfacerequired to refract the ray segment R3(-28) to intersect with thepreviously defined location of the intersection of ray segment R4(-28)and the surface PS3. Next, by extending the tangent line from thesurface PS2 at the previously defined point of intersection of the raysegment R4(-29) and the surface PS3 to intersect with the ray segmentR4(-28), the final location of the surface PS3 at the intersection ofthe ray segment R4(-28) is determined. This process of defining pointson the surface PS3 is reiterated for the light rays R3(-28), R3(-27),and so forth until ray segment R3(0) is reached and the points on thesurfaces PS3 and PS2 are known all the way to the y-axis.

Table 1 below contains four sets of 121 points on the right had side ofthe y-axis that lie on the example surfaces PS1, PS2, PS3, and PS4 shownin FIGS. 1 through 6B. Because the lenses 1 and 2 are symmetrical aboutthe y-axis, the set of points can be rotated around the y-axis todetermine other points that lie on the example surfaces PS1, PS2, PS3,and PS4. The data Table 1 can represent data having any unit and can bescaled to any desired overall size.

TABLE 1 Point Surface PS1 (x,y) Surface PS2 (x,y) Surface PS3 (x,y)Surface PS4 (x,y)  1 (9.181152,−5.300741) (3.000000,−1.732051)(0.000000,−2.053583) (0.000000,−2.307255)  2 (9.272265,−5.139700)(3.076601,−1.705207) (0.017777,−2.053577) (0.016346,−2.307489)  3(9.360553,−4.977094) (3.153488,−1.676535) (0.035537,−2.053563)(0.031245,−2.307918)  4 (9.445989,−4.812972) (3.231123,−1.646176)(0.053255,−2.053527) (0.046862,−2.308645)  5 (9.528548,−4.647384)(3.309360,−1.613921) (0.070981,−2.053470) (0.062475,−2.309372)  6(9.608205,−4.480380) (3.388147,−1.579764) (0.088727,−2.053390)(0.078085,−2.310099)  7 (9.684935,−4.312011) (3.467431,−1.543650)(0.106500,−2.053289) (0.093663,−2.312568)  8 (9.758715,−4.142329)(3.547162,−1.505535) (0.124299,−2.053164) (0.109239,−2.314454)  9(9.829522,−3.971385) (3.627286,−1.465377) (0.142134,−2.053017)(0.124799,−2.316629)  10 (9.897336,−3.799231) (3.707753,−1.423136)(0.160010,−2.052846) (0.140341,−2.319091)  11 (9.962134,−3.625920)(3.788506,−1.378763) (0.177929,−2.052651) (0.155863,−2.321840)  12(10.023898,−3.451505) (3.869506,−1.332247) (0.195898,−2.052431)(0.171363,−2.324875)  13 (10.082608,−3.276038) (3.950682,−1.283526)(0.213921,−2.052187) (0.186837,−2.328194)  14 (10.138247,−3.099573)(4.031975,−1.232573) (0.232002,−2.051916) (0.202285,−2.331796)  15(10.190798,−2.922164) (4.113324,−1.179355) (0.250148,−2.051620)(0.217704,−2.335680)  16 (10.240245,−2.743865) (4.194666,−1.123838)(0.268359,−2.051296) (0.233092,−2.339845)  17 (10.286572,−2.564730)(4.275938,−1.065995) (0.286644,−2.050944) (0.248446,−2.344289)  18(10.329766,−2.384814) (4.357071,−1.005796) (0.305004,−2.050564)(0.263765,−2.349009)  19 (10.369814,−2.204172) (4.437999,−0.943216)(0.323446,−2.050154) (0.279047,−2.354005)  20 (10.406702,−2.022858)(4.518653,−0.878231) (0.341972,−2.049713) (0.294289,−2.359274)  21(10.440421,−1.840928) (4.598956,−0.810817) (0.360586,−2.049240)(0.309490,−2.364815)  22 (10.470960,−1.658437) (4.678836,−0.740954)(0.379294,−2.048734) (0.324647,−2.370624)  23 (10.498309,−1.475441)(4.758219,−0.668627) (0.398097,−2.048194) (0.339758,−2.376700)  24(10.522460,−1.291996) (4.837026,−0.593818) (0.417002,−2.047620)(0.354823,−2.383041)  25 (10.543405,−1.108157) (4.915179,−0.516516)(0.436009,−2.047009) (0.369838,−2.389643)  26 (10.561140,−0.923980)(4.992597,−0.436709) (0.455123,−2.046360) (0.384801,−2.396504)  27(10.575657,−0.739522) (5.069198,−0.354389) (0.474347,−2.045673)(0.399712,−2.403621)  28 (10.586952,−0.554839) (5.144896,−0.269551)(0.493685,−2.044945) (0.414568,−2.410991)  29 (10.595023,−0.369986)(5.219613,−0.182196) (0.513138,−2.044176) (0.429367,−2.418611)  30(10.599867,−0.185021) (5.293258,−0.092320) (0.532710,−2.043364)(0.444109,−2.426477)  31 (10.601481, 0.000000) (5.365745,0.000070)(0.552402,−2.042507) (0.458790,−2.434587)  32 (10.599867, 0.185021)(5.436987,0.094970) (0.572219,−2.041605) (0.473410,−2.442937)  33(10.595023, 0.369986) (5.506895,0.192369) (0.592161,−2.040656)(0.487967,−2.451523)  34 (10.586952, 0.554839) (5.575380,0.292253)(0.612231,−2.039659) (0.502459,−2.460342)  35 (10.575657, 0.739522)(5.642351,0.394608) (0.632430,−2.038611) (0.516886,−2.469389)  36(10.561140, 0.923980) (5.707718,0.499414) (0.652373,−2.037490)(0.531245,−2.478661)  37 (10.543405, 1.108157) (5.771390,0.606647)(0.672844,−2.036295) (0.545535,−2.488154)  38 (10.522460, 1.291996)(5.833276,0.716282) (0.693451,−2.035046) (0.559755,−2.497863)  39(10.498309, 1.475441) (5.893285,0.828289) (0.714191,−2.033744)(0.573904,−2.507785)  40 (10.470960, 1.658437) (5.951326,0.942636)(0.735069,−2.032385) (0.587980,−2.517914)  41 (10.440421, 1.840928)(6.007308,1.059285) (0.756082,−2.030970) (0.601983,−2.528247)  42(10.406702, 2.022858) (6.061141,1.178198) (0.777233,−2.029497)(0.615911,−2.538779)  43 (10.369814, 2.204172) (6.112735,1.299329)(0.798521,−2.027964) (0.629763,−2.549505)  44 (10.329766, 2.384814)(6.162000,1.422634) (0.819946,−2.026372) (0.643538,−2.560420)  45(10.286572, 2.564730) (6.208847,1.548060) (0.841508,−2.024719)(0.657236,−2.571521)  46 (10.240245, 2.743865) (6.253191,1.675554)(0.863207,−2.023004) (0.670855,−2.582801)  47 (10.190798, 2.922164)(6.294943,1.805059) (0.885041,−2.021227) (0.684395,−2.594257)  48(10.138247, 3.099573) (6.334018,1.936513) (0.907015,−2.019386)(0.697855,−2.605883)  49 (10.082608, 3.276038) (6.370334,2.069853)(0.929115,−2.017482) (0.711235,−2.617674)  50 (10.023898, 3.451505)(6.403807,2.205010) (0.951352,−2.015514) (0.724533,−2.629625)  51(9.962134, 3.625920) (6.434359,2.341913) (0.973740,−2.013481)(0.737749,−2.641732)  52 (9.897336, 3.799231) (6.461908,2.480489)(0.996219,−2.011386) (0.750883,−2.653988)  53 (9.829522, 3.971385)(6.486379,2.620658) (1.018885,−2.009223) (0.763934,−2.666390)  54(9.758715, 4.142329) (6.507697,2.762341) (1.041600,−2.007000)(0.776902,−2.678933)  55 (9.684935, 4.312011) (6.525791,2.905453)(1.064479,−2.004709) (0.789786,−2.691610)  56 (9.608205, 4.480380)(6.540591,3.049908) (1.087481,−2.002353) (0.802586,−2.704417)  57(9.528548, 4.647384) (6.552029,3.195615) (1.110603,−1.999934)(0.815302,−2.717350)  58 (9.445989, 4.812972) (6.560042,3.342482)(1.133843,−1.997452) (0.827934,−2.730402)  59 (9.360553, 4.977094)(6.564567,3.490412) (1.154751,−1.995053) (0.840482,−2.743570)  60(9.272265, 5.139700) (6.565546,3.639309) (1.180725,−1.992167)(0.852945,−2.756848)  61 (9.181152, 5.300741) (6.562926,3.789070)(1.204304,−1.989499) (0.865323,−2.770231)  62 (9.087243, 5.460167)(6.556645,3.939592) (1.227992,−1.986771) (0.877617,−2.783715)  63(8.990566, 5.617929) (6.546685,4.090765) (1.251784,−1.983983)(0.889826,−2.797294)  64 (8.891150, 5.773981) (6.532895,4.242480)(1.275678,−1.981138) (0.901951,−2.810965)  65 (8.789026, 5.928273)(6.515398,4.394640) (1.299669,−1.978237) (0.913991,−2.824722)  66(8.684225, 6.080760) (6.494050,4.547131) (1.323757,−1.975281)(0.925948,−2.838560)  67 (8.576779, 6.231394) (6.468845,4.699835)(1.347935,−1.972271) (0.937820,−2.852476)  68 (8.466720, 6.380131)(6.439745,4.852637) (1.372205,−1.969209) (0.949608,−2.866465)  69(8.354081, 6.526924) (6.406724,5.005420) (1.396559,−1.966097)(0.961313,−2.880522)  70 (8.238899, 6.671728) (6.369760,5.158066)(1.420994,−1.962937) (0.972935,−2.894644)  71 (8.121206, 6.814501)(6.328833,5.310454) (1.445510,−1.959731) (0.984474,−2.908825)  72(8.001040, 6.955198) (6.283929,5.462466) (1.470177,−1.956472)(0.995930,−2.923062)  73 (7.878436, 7.093776) (6.235036,5.613980)(1.494765,−1.953189) (1.007304,−2.937351)  74 (7.753433, 7.230193)(6.182149,5.764872) (1.519494,−1.949855) (1.018596,−2.951689)  75(7.626068, 7.364408) (6.125265,5.915022) (1.544290,−1.946482)(1.029807,−2.966070)  76 (7.496379, 7.496379) (6.064385,6.064305)(1.569151,−1.943073) (1.040937,−2.980491)  77 (7.364408, 7.626068)(5.999517,6.212599) (1.594068,−1.939630) (1.051987,−2.994950)  78(7.230193, 7.753433) (5.930670,6.359780) (1.619042,−1.936154)(1.062957,−3.009441)  79 (7.093776, 7.878436) (5.857858,6.505724)(1.644070,−1.932649) (1.073847,−3.023962)  80 (6.955198, 8.001040)(5.781102,6.650309) (1.669143,−1.929117) (1.084658,−3.038510)  81(6.814501, 8.121206) (5.700425,6.793411) (1.694264,−1.925559)(1.095391,−3.053080)  82 (6.671728, 8.238898) (5.615853,6.934908)(1.719427,−1.921978) (1.106046,−3.067670)  83 (6.526924, 8.354081)(5.527419,7.074678) (1.744628,−1.918376) (1.116624,−3.082278)  84(6.380131, 8.466720) (5.435158,7.212602) (1.769868,−1.914755)(1.127125,−3.096899)  85 (6.231394, 8.576779) (5.339111,7.348558)(1.795138,−1.911119) (1.137550,−3.111531)  86 (6.080760, 8.684225)(5.239324,7.482429) (1.820439,−1.907468) (1.147899,−3.126171)  87(5.928273, 8.789026) (5.135839,7.614096) (1.845767,−1.903806)(1.158173,−3.140816)  88 (5.773981, 8.891150) (5.028725,7.743454)(1.871120,−1.900133) (1.168374,−3.155465)  89 (5.617929, 8.990566)(4.918023,7.870377) (1.896492,−1.896454) (1.178500,−3.170113)  90(5.460167, 9.087243) (4.803797,7.994755) (1.921885,−1.892769)(1.188553,−3.184760)  91 (5.300741,9.181152) (4.686112,8.116477)(1.947292,−1.889083) (1.198534,−3.199402)  92 (5.139700, 9.272265)(4.565036,8.235433) (1.972711,−1.885394) (1.208443,−3.214037)  93(4.977094, 9.360553) (4.440640,8.351518) (1.998145,−1.881705)(1.218281,−3.228663)  94 (4.812972, 9.445989) (4.313000,8.464628)(2.023584,−1.878019) (1.228049,−3.243279)  95 (4.647384, 9.528548)(4.182196,8.574660) (2.048696,−1.874381) (1.237746,−3.257881)  96(4.480380, 9.608205) (4.048310,8.681515) (2.074342,−1.870675)(1.247375,−3.272468)  97 (4.312011, 9.684935) (3.911428,8.785096)(2.099937,−1.866988) (1.256934,−3.287039)  98 (4.142329, 9.758715)(3.771640,8.885310) (2.125386,−1.863333) (1.266426,−3.301590)  99(3.971385, 9.829522) (3.629037,8.982066) (2.150829,−1.859689)(1.275850,−3.316121) 100 (3.799231, 9.897336) (3.483717,9.075275)(2.176273,−1.856059) (1.285208,−3.330631) 101 (3.625920, 9.962134)(3.335777,9.164852) (2.201637,−1.852439) (1.294500,−3.345116) 102(3.451505,10.023898) (3.185319,9.250717) (2.227133,−1.848843)(1.303726,−3.359577) 103 (3.276038,10.082608) (3.032447,9.332790)(2.252834,−1.845241) (1.312887,−3.374011) 104 (3.099573,10.138247)(2.877267,9.410995) (2.277935,−1.841723) (1.321985,−3.388417) 105(2.922164,10.190798) (2.719891,9.485263) (2.303318,−1.838184)(1.331019,−3.402793) 106 (2.743865,10.240245) (2.560428,9.555523)(2.328695,−1.834666) (1.339990,−3.417140) 107 (2.564730,10.286572)(2.398994,9.621712) (2.354048,−1.831172) (1.348898,−3.431454) 108(2.384814,10.329766) (2.235704,9.683769) (2.379374,−1.827704)(1.357745,−3.445735) 109 (2.204172,10.369814) (2.070676,9.741636)(2.404687,−1.824260) (1.366532,−3.459983) 110 (2.022858,10.406702)(1.904031,9.795261) (2.430114,−1.820801) (1.375257,−3.474195) 111(1.840928,10.440421) (1.735891,9.844594) (2.455303,−1.817446)(1.383923,−3.488372) 112 (1.658437,10.470960) (1.566378,9.889588)(2.475715,−1.814679) (1.392530,−3.502512) 113 (1.475441,10.498309)(1.395618,9.930204) (2.501099,−1.811266) (1.401078,−3.516614) 114(1.291996,10.522460) (1.223737,9.966402) (2.526406,−1.807891)(1.409568,−3.530676) 115 (1.108157,10.543405) (1.050863,9.998151)(2.551489,−1.804569) (1.418002,−3.544696) 116 (0.923980,10.561140)(0.877124,10.025416) (2.576437,−1.801288) (1.426379,−3.558678) 117(0.739522,10.575657) (0.702648,10.048188) (2.601558,−1.798008)(1.434698,−3.572622) 118 (0.554839,10.586952) (0.527568,10.066393)(2.628641,−1.794518) (1.442959,−3.586532) 119 (0.369986,10.595023)(0.352012,10.080206) (2.657369,−1.790883) (1.451165,−3.600401) 120(0.185021,10.599867) (0.176116,10.088896) (2.681569,−1.787826)(1.459319,−3.614217) 121 (0.000000,10.601481) (0.000000,10.093058)(2.705059,−1.784856) (1.467426,−3.627971)

According to the embodiment illustrated in FIGS. 1-6B, the surface PS1is semispherical. Thus, the surface PS1 can be approximated by a set ofpoints (x, y, z) defined by Equation 2, where the center of the sphereis (x₀, y₀, and z₀) and the radius of the sphere is r.

r ²=(x−x ₀)²+(y−y ₀)²+(z−z ₀)²   Equation 2

The surface PS3 can be approximated by a set of points (x, y) defined bythe sixth-order polynomial of Equation 3. The polynomial of Equation 3was derived from the data in Table 1. While the set of points (x, y) canbe approximated by a sixth-order polynomial, a polynomial having a loweror higher order may be used. Additionally, the surface PS3 may beapproximated by or be defined by another equation.

y=−0.000044x ⁶+0.003106x ⁵−0.022809x ⁴+0.049379x ³+0.009716x²+0.003407x−2.053740   Equation 3

According to the embodiment illustrated in FIGS. 1-6B, the surface PS4takes the same Harris shape as the imaginary picture plane IPP along atleast a portion of the cross-section. The surface PS4 can beapproximated by a set of points (x, y) defined by the sixth-orderpolynomial of Equation 4. The polynomial of Equation 4 was derived fromthe data in Table 1. While the set of points (x, y) can be approximatedby a sixth-order polynomial, a polynomial having a lower or higher ordermay be used. Additionally, the surface PS4 may be approximated by or bedefined by another equation.

y=−0.031617x ⁶+0.157514x ⁵−0.230715x ⁴+0.105277x ³−0.623794x²+0.002439x−2.307265   Equation 4

Reflective Lenses

Whereas a camera using the refractive lens may be located below the lensnear the camera point CP2, as shown in FIG. 1, a camera using areflective lens may be located above the lens near a camera point CP1,as shown in FIG. 7. In certain embodiments, the images captured usingthe refractive and reflective lenses are identical with the possibleexception that the camera itself may be seen in the image captured usingthe reflective lens.

With reference to FIG. 7, light rays, depicted by arrows distributedfrom −30 degrees to 90 degrees about station point SP, intersect asurface PSH and are reflected to the camera point CP1. In other words,all the light rays within the field of view heading toward the stationpoint SP are reflected toward the camera point CP1. A flat image may bephotographically or digitally stored at a focal plane or viewing planeVP1 as previously described with reference to FIGS. 1 through 6. Asviewed in cross-section, if the extent of the image as viewed fromcamera point CP1 is divided into equal angular increments, and theextent of the image as viewed from the station point SP is divided bythe same number of equal angular increments then the cross-sectionalsurface of a Harris shape may be defined by the intersections of theindividual lines representing the angular increments converging on thestation point SP with the respective individual lines representing theangular increments that converge on camera point CP1. A Harris shapethree dimensional surface may be defined when this cross-section isrotated about the central axis containing the station point SP andcamera point CP1. The Harris shape results in an image having a uniformdensity as experienced by the viewer, located at the station point SP,across the entire viewing surface.

Referring to FIG. 8, the light rays heading to the station point SP arereflected to the camera point CP1 and a two dimensional flat image iscaptured at the viewing plane VP1. The reflective lens may be made fromsteel using a computer numerically controlled (CNC) metal lathe processand plated with chrome to provide reflectivity. The camera used can befilm or digital, and can collect still or moving images.

FIG. 9 illustrates a detailed cross-section of point PH(-30) of FIG. 8.The ray R1(-30) was heading to the station point SP in the AIR at 30degrees below the x-axis. After the ray intersects with the surface PSH,it is redirected toward the camera point CP1. The ray R1 indicates a rayof light, in the AIR, prior to intersection of the surface PSH and theray R2 designates the ray of light, in the AIR, after the intersectionat the reflective surface PSH. The neutral line N is perpendicular toline T. The line T is the tangent line to the surface PS1 at pointPS(-30). The line H is the horizontal line or x-axis. The angle from thelight ray R1(-30) to the vertical line V is LVA. The angle from thelight ray R1(-30) to the neutral line N is LNA. The angle from the lightray R1(-30) to the horizontal line H is RHA. The angle from the lightray R2(-30) to the vertical line V is RVA.

Table 2 below contains a set of 121 points on the right had side of they-axis that lie on an example surface PSH shown in FIG. 7. Because thesurface PSH is symmetrical about the y-axis, the set of points can berotated around the y-axis to determine other points that lie on theexample surface PSH. The data Table 2 can represent data having any unitand can be scaled to any desired overall size.

TABLE 2 Point Surface PSH (x,y)   1 (3.000000,−1.732051)   2(2.939252,−1.629254)   3 (2.880914,−1.531809)   4 (2.824805,−1.439310)  5 (2.770761−1.351391)   6 (2.718635,−1.267720)   7(2.668293,−1.188001)   8 (2.619613,−1.111960)   9 (2.572485,−1.039351) 10 (2.526808,−0.969951)  11 (2.482490,−0.903552)  12(2.439447,−0.839969)  13 (2.397601,−0.779028)  14 (2.356882,−0.720571) 15 (2.317223,−0.664453)  16 (2.278565,−0.610540)  17(2.240851,−0.558707)  18 (2.204030,−0.508841)  19 (2.168054,−0.460834) 20 (2.132879,−0.414590)  21 (2.098463,−0.370016)  22(2.064767,−0.327027)  23 (2.031755,−0.285545)  24 (1.999395,−0.245495) 25 (1.967655,−0.206809)  26 (1.936505,−0.169422)  27(1.905918,−0.133275)  28 (1.875868,−0.098310)  29 (1.846331,−0.064475) 30 (1.817284,−0.031721)  31 (1.788705,0.000000)  32 (1.760576,0.030731) 33 (1.732875,0.060513)  34 (1.705586,0.089386)  35 (1.678692,0.117386) 36 (1.652176,0.144547)  37 (1.626023,0.170902)  38 (1.600219,0.196482) 39 (1.574749,0.221317)  40 (1.549602,0.245433)  41 (1.524765,0.268857) 42 (1.500226,0.291614)  43 (1.475973,0.313728)  44 (1.451997,0.335220) 45 (1.428287,0.356112)  46 (1.404833,0.376424)  47 (1.381626,0.396175) 48 (1.358658,0.415384)  49 (1.335921,0.434067)  50 (1.313405,0.452241) 51 (1.291103,0.469923)  52 (1.269008,0.487127)  53 (1.247113,0.503866) 54 (1.225412,0.520156)  55 (1.203896,0.536009)  56 (1.182561,0.551437) 57 (1.161401,0.566453)  58 (1.140409,0.581067)  59 (1.119580,0.595291) 60 (1.098909,0.609135)  61 (1.078390,0.622609)  62 (1.058019,0.635722) 63 (1.037791,0.648484)  64 (1.017701,0.660903)  65 (0.997745,0.672987) 66 (0.977918,0.684745)  67 (0.958216,0.696185)  68 (0.938636,0.707313) 69 (0.919173,0.718137)  70 (0.899824,0.728663)  71 (0.880584,0.738898) 72 (0.861451,0.748848)  73 (0.842421,0.758520)  74 (0.823491,0.767918) 75 (0.804657,0.777048)  76 (0.785917,0.785917)  77 (0.767266,0.794527) 78 (0.748703,0.802886)  79 (0.730224,0.810996)  80 (0.711827,0.818863) 81 (0.693509,0.826491)  82 (0.675266,0.833884)  83 (0.657098,0.841047) 84 (0.639000,0.847981)  85 (0.620970,0.854692)  86 (0.603007,0.861183) 87 (0.585108,0.867458)  88 (0.567269,0.873518)  89 (0.549490,0.879368) 90 (0.531768,0.885011)  91 (0.514100,0.890448)  92 (0.496485,0.895683) 93 (0.478921,0.900719)  94 (0.461405,0.905557)  95 (0.443935,0.910201) 96 (0.426509,0.914652)  97 (0.409126,0.918912)  98 (0.391784,0.922984) 99 (0.374480,0.926869) 100 (0.357212,0.930570) 101 (0.339980,0.934087)102 (0.322781,0.937423) 103 (0.305613,0.940579) 104 (0.288474,0.943556)105 (0.271363,0.946356) 106 (0.254279,0.948981) 107 (0.237218,0.951430)108 (0.220180,0.953706) 109 (0.203164,0.955809) 110 (0.186166,0.957741)111 (0.169186,0.959502) 112 (0.152222,0.961093) 113 (0.135273,0.962514)114 (0.118336,0.963767) 115 (0.101410,0.964852) 116 (0.084494,0.965769)117 (0.067586,0.966518) 118 (0.050684,0.967101) 119 (0.033786,0.967517)120 (0.016892,0.967767) 121 (0.000000,0.968016)

The surface PSH can be approximated by a set of points (x, y) defined bythe sixth-order polynomial of Equation 5. The polynomial of Equation 5was derived from the data in Table 2. While the set of points (x, y) canbe approximated by a sixth-order polynomial, a polynomial having a loweror higher order may be used. Additionally, the surface PS3 may beapproximated by or be defined by another equation.

y=−0.0007x ⁶+0.0077x ⁵−0.0226x ⁴+0.0184x ³−0.3006x ²+0.0017x+0.9678  Equation 5

With reference to FIG. 8, the Harris shape may be defined inmathematical terms by rotating the cross-sectional surface defined inEquation 22, about the SP-CP axis. Equation 22 can be used to determinethe coordinates of a plurality of points on a cross-section of theHarris shape. A derivation for Equation 22 will be described in moredetail with respect to Equation 6 through Equation 21. As shown inEquation 6, the angle RVA is calculated from the arctangent of thechange in X over the change in Y. With respect to Equation 6 and FIG. 9,X_(CP1) and Y_(CP1) refer to the X,Y coordinates of the camera point CP1and X_(PSH) and Y_(PSH) refer to the X,Y coordinates of a point on thesurface PSH.

$\begin{matrix}{{{RVA}_{e} = {a\; {Tan}\; \left( \frac{X_{{CP}\; 1} - X_{e}}{Y_{{CP}\; 1} - Y_{e}} \right)}}\;} & {{Equation}\mspace{14mu} 6}\end{matrix}$

As shown in Equation 7, the angle LHA is calculated from the arctangentof the change in Y over the change in X. With respect to Equation 7 andFIG. 9, X_(SP) and Y_(SP) refer to the X,Y coordinates of the stationpoint SP and X_(PSH) and Y_(PSH) refer to the X,Y coordinates of a pointon the surface PSH.

$\begin{matrix}{{LHA} = {a\; {{Tan}\left( \frac{Y_{SP} - Y_{PSH}}{X_{PSH} - X_{SP}} \right)}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

Equation 8 and Equation 9 can be used to define any light ray segment R1within the field of view and headed to the station point SP, whereX_(PSH) and Y_(PSH) represent a X and Y coordinate of a point on theline, M represents the slope of the line and b represents theintersection of the line with the y-axis.

Y=M×X+b   Equation 8

Equation 9 refines Equation 8 to represent the ray segment R1.

Y _(e)=Tan(LHA)×X _(e) +Y _(SP)   Equation 9

Equation 8 and Equation 10 can be used to define a reflective raysegment R2 corresponding to the ray segment R1 within the field of viewand headed to the camera point CP, where Y represents a Y coordinate ofa point on the line, X represents the X coordinate of that same point, Mrepresents the slope of the line and b represents the intersection ofthe line with the y-axis. Equation 10 refines Equation 8 to representthe ray segment R2.

Y _(e)=Tan(RVA)×X _(e) +Y _(CP1)   Equation 10

Equation 11 shows that X_(PSH), can be determined from combiningEquation 9, which depicts the coordinate Y_(PSH) of the ray segment R1,with Equation 10, which depicts the coordinate Y_(PSH) of the raysegment R2.

Tan(LHA)×X _(e) +Y _(SP)=Tan(RVA)×X _(e) +Y _(CP1)   Equation 11

Equation 12 is determined by substitution, and since the origin of thecoordinate system is at the station point SP (Xsp,Ysp)=(0,0), and Xcp1=0as it is located on the x axis.

$\begin{matrix}{{{{{Tan}\left( {a\; {{Tan}\left( \frac{Y_{SP} - Y_{PSH}}{X_{PSH} - X_{SP}} \right)}} \right)} \times {Xpsh}} + {Ysp}} = {{Tan}\left( {{\left( {{a\; {Tan}\mspace{11mu} \left( \frac{X_{e} - X_{{CP}\; 1}}{Y_{{CP}\; 1} - Y_{e}} \right)} - {n \times \Delta \; F_{RVA}}} \right)\left. \quad{- 90^{*}} \right) \times {Xpsh}} + {{Ycp}\; 1}} \right.}} & {{Equation}\mspace{14mu} 12} \\{{{\left( \frac{Y_{SP} - Y_{PSH}}{X_{PSH} - X_{SP}} \right) \times {Xpsh}} + {Ysp}} = {{{Tan}\mspace{11mu} \left( {{a\; {Tan}\mspace{11mu} \left( \frac{X_{{CP}\; 1} - X_{e}}{Y_{{CP}\; 1} - Y_{e}} \right)} - {n \times \Delta \; F_{RVA}}} \right) \times {Xpsh}} + {{Ycp}\; 1}}} & {{Equation}\mspace{14mu} 13} \\{{{\left( \frac{Y_{SP} - Y_{PSH}}{X_{PSH} - X_{SP}} \right) \times {Xpsh}} - {\left( {\left( \frac{X_{{CP}\; 1} - X_{e}}{Y_{{CP}\; 1} - Y_{e}} \right) - {n \times \Delta \; F_{RVA}}} \right) \times {Xpsh}}} = {{{Ycp}\; 1} - {Ysp}}} & {{Equation}\mspace{14mu} 14} \\{{\left( {\frac{Y_{SP} - Y_{PSH}}{X_{PSH} - X_{SP}} - \frac{{{Xcp}\; 1} - {Xe}}{{{Ycp}\; 1} - {Ye}} + \left( {n \times \Delta \; {Frva}} \right)} \right) \times {Xpsh}} = {{{Ycp}\; 1} - {Ysp}}} & {{Equation}\mspace{14mu} 15} \\{{Xpsh} = \frac{\left( {{{Ycp}\; 1} - {Ysp}} \right)}{\frac{Y_{SP} - Y_{PSH}}{X_{PSH} - X_{SP}} - \frac{{{Xcp}\; 1} - {Xe}}{{{Ycp}\; 1} - {Ye}} + \left( {n \times \Delta \; {Frva}} \right)}} & {{Equation}\mspace{14mu} 16} \\{{Xpsh} = \frac{\left( {{{Ycp}\; 1} - {Ysp}} \right)}{\frac{{\left( {Y_{SP} - Y_{PSH}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)} - {\left( {{{Xcp}\; 1} - {Xe}} \right) \times \left( {X_{PSH} - X_{SP}} \right)} + {\left( {n \times \Delta \; {Frva}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}}{\left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}}} & {{Equation}\mspace{14mu} 17} \\{{Xpsh} = \frac{\left( {{{Ycp}\; 1} - {Ysp}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}{{\left( {Y_{SP} - Y_{PSH}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)} - {\left( {{{Xcp}\; 1} - {Xe}} \right) \times \left( {X_{PSH} - X_{SP}} \right)} + {\left( {n \times \Delta \; {Frva}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}}} & {{Equation}\mspace{14mu} 18} \\{\left( \frac{1}{Xpsh} \right) = \frac{{\left( {Y_{SP} - Y_{PSH}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)} - {\left( {{{Xcp}\; 1} - {Xe}} \right) \times \left( {X_{PSH} - X_{SP}} \right)} + {\left( {n \times \Delta \; {Frva}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}}{\left( {{{Ycp}\; 1} - {Ysp}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}} & {{Equation}\mspace{14mu} 19} \\{\left( \frac{\left( {{{Ycp}\; 1} - {Ysp}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}{Xpsh} \right) = {{\left( {Y_{SP} - Y_{PSH}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)} - {\left( {{{Xcp}\; 1} - {Xe}} \right) \times \left( {X_{PSH} - X_{SP}} \right)} + {\left( {n \times \Delta \; {Frva}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}}} & {{Equation}\mspace{14mu} 20} \\{{\left( \frac{\left( {{{Ycp}\; 1} - {Ysp}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}{Xpsh} \right) + {\left( {{{Xcp}\; 1} - {Xe}} \right) \times \left( {X_{PSH} - X_{SP}} \right)} - {\left( {n \times \Delta \; {Frva}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}} = {\left( {Y_{SP} - Y_{PSH}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}} & {{Equation}\mspace{14mu} 21} \\{Y_{PSH} = {Y_{SP} - \frac{\left( \frac{\left( {{{Ycp}\; 1} - {Ysp}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}{Xpsh} \right) + {\left( {{{Xcp}\; 1} - {Xe}} \right) \times \left( {X_{PSH} - X_{SP}} \right)} - {\left( {n \times \Delta \; {Frva}} \right) \times \left( {X_{PSH} - X_{SP}} \right) \times \left( {{{Ycp}\; 1} - {Ye}} \right)}}{\left( {{{Ycp}\; 1} - {Ye}} \right)}}} & {{Equation}\mspace{14mu} 22}\end{matrix}$

As the value of n changes, points on the cross-section of the surfacePSH are defined. In this example, Equation 22, with n=5, would appear asEquation 23 when solving for Ypsh for the illustrative embodiment.

$\begin{matrix}{Y_{PSH} = {0 - \frac{\left( \frac{\left( {7.2679 - 0} \right) \times \left( {X_{PSH} - 0} \right) \times \left( {{7.2679--}1.7321} \right)}{X_{PSH}} \right) + {\left( {0 - 3} \right) \times \left( {X_{PSH} - 0} \right)} - {\left( {5 \times \frac{RVAe}{D}} \right) \times \left( {X_{PSH} - 0} \right) \times \left( {X_{PSH} - 0} \right) \times \left( {{7.2679--}1.7321} \right)}}{\left( {{7.2679--}1.7321} \right)}}} & {{Equation}\mspace{14mu} 23} \\{Y_{PSH} = {0 - \frac{\left( \frac{(7.2679) \times \left( X_{PSH} \right) \times (9)}{Xpsh} \right) + {\left( {- 3} \right) \times \left( X_{PSH} \right)} - {\left( {5 \times \frac{18.4348}{120}} \right) \times \left( X_{PSH} \right) \times (9)}}{(9)}}} & {{Equation}\mspace{14mu} 24} \\{Y_{PSH} = {{- (7.2679)} - {\left( \frac{3}{9} \right) \times \left( X_{PSH} \right)} - {\left( {5 \times \frac{18.4348}{120}} \right) \times \left( X_{PSH} \right)}}} & {{Equation}\mspace{14mu} 25} \\{Y_{PSH} = {\left( {{- (7.2679)} - \left( \frac{3}{9} \right) - \left( {5 \times \frac{18.4348}{120}} \right)} \right) \times \left( X_{PSH} \right)}} & {{Equation}\mspace{14mu} 26}\end{matrix}$

Table 3 below contains a set of points derived from the example above onthe right hand side of the y-axis that lie on the surface PSH of FIG. 7.In particular, Table 3 contains a set of 121 points that lie on thesurface PSH. Because the surface PSH is symmetrical about the y-axis,the set of points can be rotated around the y-axis to determine otherpoints that lie on the surface PSH. The data in Table 3 can representdata having any unit and can be scaled to any desired overall size.

TABLE 3 LHA ( ) RVA ( ) X Y −30.0000 18.4349 3.000000 −1.732051 −29.000018.2813 2.939252 −1.629254 −28.0000 18.1277 2.880914 −1.531809 −27.000017.9741 2.824805 −1.439310 −26.0000 17.8205 2.770761 −1.351391 −25.000017.6668 2.718635 −1.267720 −24.0000 17.5132 2.668293 −1.188001 −23.000017.3596 2.619613 −1.111960 −22.0000 17.2060 2.572485 −1.039351 −21.000017.0523 2.526808 −0.969951 −20.0000 16.8987 2.482490 −0.903552 −19.000016.7451 2.439447 −0.839969 −18.0000 16.5915 2.397601 −0.779028 −17.000016.4378 2.356882 −0.720571 −16.0000 16.2842 2.317223 −0.664453 −15.000016.1306 2.278565 −0.610540 −14.0000 15.9770 2.240851 −0.558707 −13.000015.8233 2.204030 −0.508841 −12.0000 15.6697 2.168054 −0.460834 −11.000015.5161 2.132879 −0.414590 −10.0000 15.3625 2.098463 −0.370016 −9.000015.2088 2.064767 −0.327027 −8.0000 15.0552 2.031755 −0.285545 −7.000014.9016 1.999395 −0.245495 −6.0000 14.7480 1.967655 −0.206809 −5.000014.5943 1.936505 −0.169422 −4.0000 14.4407 1.905918 −0.133275 −3.000014.2871 1.875868 −0.098310 −2.0000 14.1335 1.846331 −0.064475 −1.000013.9798 1.817284 −0.031721 0.0000 13.8262 1.788705 0.000000 1.000013.6726 1.760576 0.030731 2.0000 13.5190 1.732875 0.060513 3.000013.3653 1.705586 0.089386 4.0000 13.2117 1.678692 0.117386 5.000013.0581 1.652176 0.144547 6.0000 12.9045 1.626023 0.170902 7.000012.7508 1.600219 0.196482 8.0000 12.5972 1.574749 0.221317 9.000012.4436 1.549602 0.245433 10.0000 12.2900 1.524765 0.268857 11.000012.1363 1.500226 0.291614 12.0000 11.9827 1.475973 0.313728 13.000011.8291 1.451997 0.335220 14.0000 11.6755 1.428287 0.356112 15.000011.5218 1.404833 0.376424 16.0000 11.3682 1.381626 0.396175 17.000011.2146 1.358658 0.415384 18.0000 11.0610 1.335921 0.434067 19.000010.9073 1.313405 0.452241 20.0000 10.7537 1.291103 0.469923 21.000010.6001 1.269008 0.487127 22.0000 10.4465 1.247113 0.503866 23.000010.2928 1.225412 0.520156 24.0000 10.1392 1.203896 0.536009 25.00009.9856 1.182561 0.551437 26.0000 9.8320 1.161401 0.566453 27.0000 9.67831.140409 0.581067 28.0000 9.5247 1.119580 0.595291 29.0000 9.37111.098909 0.609135 30.0000 9.2175 1.078390 0.622609 31.0000 9.06381.058019 0.635722 32.0000 8.9102 1.037791 0.648484 33.0000 8.75661.017701 0.660903 34.0000 8.6030 0.997745 0.672987 35.0000 8.44940.977918 0.684745 36.0000 8.2957 0.958216 0.696185 37.0000 8.14210.938636 0.707313 38.0000 7.9885 0.919173 0.718137 39.0000 7.83490.899824 0.728663 40.0000 7.6812 0.880584 0.738898 41.0000 7.52760.861451 0.748848 42.0000 7.3740 0.842421 0.758520 43.0000 7.22040.823491 0.767918 44.0000 7.0667 0.804657 0.777048 45.0000 6.91310.785917 0.785917 46.0000 6.7595 0.767266 0.794527 47.0000 6.60590.748703 0.802886 48.0000 6.4522 0.730224 0.810996 49.0000 6.29860.711827 0.818863 50.0000 6.1450 0.693509 0.826491 51.0000 5.99140.675266 0.833884 52.0000 5.8377 0.657098 0.841047 53.0000 5.68410.639000 0.847981 54.0000 5.5305 0.620970 0.854692 55.0000 5.37690.603007 0.861183 56.0000 5.2232 0.585108 0.867458 57.0000 5.06960.567269 0.873518 58.0000 4.9160 0.549490 0.879368 59.0000 4.76240.531768 0.885011 60.0000 4.6087 0.514100 0.890448 61.0000 4.45510.496485 0.895683 62.0000 4.3015 0.478921 0.900719 63.0000 4.14790.461405 0.905557 64.0000 3.9942 0.443935 0.910201 65.0000 3.84060.426509 0.914652 66.0000 3.6870 0.409126 0.918912 67.0000 3.53340.391784 0.922984 68.0000 3.3797 0.374480 0.926869 69.0000 3.22610.357212 0.930570 70.0000 3.0725 0.339980 0.934087 71.0000 2.91890.322781 0.937423 72.0000 2.7652 0.305613 0.940579 73.0000 2.61160.288474 0.943556 74.0000 2.4580 0.271363 0.946356 75.0000 2.30440.254279 0.948981 76.0000 2.1507 0.237218 0.951430 77.0000 1.99710.220180 0.953706 78.0000 1.8435 0.203164 0.955809 79.0000 1.68990.186166 0.957741 80.0000 1.5362 0.169186 0.959502 81.0000 1.38260.152222 0.961093 82.0000 1.2290 0.135273 0.962514 83.0000 1.07540.118336 0.963767 84.0000 0.9217 0.101410 0.964852 85.0000 0.76810.084494 0.965769 86.0000 0.6145 0.067586 0.966518 87.0000 0.46090.050684 0.967101 88.0000 0.3072 0.033786 0.967517 89.0000 0.15360.016892 0.967767 90.0000 0.0000 0.000000 0.968016

The surface PSH can be approximated by a set of points (x, y) defined bythe sixth-order polynomial of Equation 27. The polynomial of Equation 27was derived from the data in Table 3. While the set of points (x, y) canbe approximated by a sixth-order polynomial, a polynomial having a loweror higher order may be used. Additionally, the surface PS3 may beapproximated by or be defined by another equation.

y=−0.0007x ⁶+0.0077x ⁵−0.0226x ⁴+0.0184x ³−0.3006x ²+0.0017x+0.9678  Equation 27

Image Generation

FIG. 10A illustrates one example of an anamorphic image (i.e., an imagedistorted in certain respects, such as aspect ratio, magnification,skew, interior angle(s), straightness, or curvature) on a viewing planeVP1 being projected onto a viewing surface PSH. FIG. 11A illustrates anexample of an anamorphic image that might be collected at the viewingplane VP1 (FIG. 7) or the viewing plane VP2 (FIG. 1) (e.g., FIG. 11Aillustrates how the anamorphic image would appear if displayed on atraditional monitor). In other words, an image captured on the viewingplane VP1 (FIG. 7) or the viewing plane VP2 (FIG. 1) is two-dimensionaland flat. When an anamorphic image captured at the viewing plane VP1 orVP2 is projected onto a viewing surface PSH (e.g., having the shapedepicted in FIG. 12A), the projected image is elongated where itintersects the viewing surface PSH at an angle and the projected imageon the viewing surface PSH is foreshortened as viewed from the stationpoint SP, resulting in an image having a uniform density for the pointof view of a viewer at the station point SP.

As previously described, an anamorphic image captured at the viewingplane VP1 (FIG. 7) or the viewing plane VP2 (FIG. 1) can spanapproximately 120 zenith degrees (e.g., have an approximately 240 degreevertical field of view). FIG. 11A illustrates a horizon line Hrepresenting the horizon in a captured image. According to oneembodiment, the distance between the station point SP (e.g., theintersection of the Z-axis and the X-axis illustrated in FIG. 11A) andthe horizon line H is two-fifths (0.4) of the distance from the stationpoint SP and the edge of the field of view (e.g., the edge of the imageillustrated in FIG. 11A). The area of the circular ring bound by thehorizon line H and the edge of the field of view is equal toπ*(r²−(0.4r)²), where r is equal to the radius to the edge of the fieldof view. Thus, the area of the image captured that is below the horizonline (i.e., the area of the circular ring bound by the horizon line Hand the edge of the field of view) measured as a percentage of the totalarea captured, is equal to (π*(r²−(0.4r)²))/(π*r²), or approximately 84percent of the total area captured.

FIG. 11B illustrates an anamorphic image that might be captured using ahypothetical fisheye lens. Although the image captured using a fisheyelens may span approximately 110 zenith degrees (e.g., have anapproximately 220 degree vertical field of view) the distance betweenthe station point SP (e.g., the intersection of the z-axis and thex-axis) and the horizon line H is approximately four-fifths (0.8) of thedistance from the station point SP and the edge of the field of view.The area of the circular ring bound by the horizon line H and the edgeof the field of view is equal to π*(r²−(0.8r)²), where r is equal to theradius to the edge of the field of view. Thus, as a percentage of thetotal area captured, the area of the circular ring bound by the horizonline H and the edge of the field of view is equal to(π*(r²−(0.8r)²))/(π*r²), or approximately 36 percent of the total areacaptured.

Thus, an anamorphic image captured at the viewing plane VP1 (FIG. 7) orthe viewing plane VP2 (FIG. 1) would contain more image detail betweenthe horizon line H and the edge of the field of view as compared to animage captured using a fisheye lens (e.g., approximately 84 percent ofthe total area captured compared to approximately 36 percent using ahypothetical fisheye lens). In other words, a fisheye lens would capturemore of the sky than an image captured at the viewing plane VP1 (FIG. 7)or the viewing plane VP2 (FIG. 1). Comparing FIG. 11B to FIG. 11Aillustrates that an image captured using the hypothetical fisheye lenswould be more distorted due to the additional image compression betweenthe horizon line H and the edge of the field of view.

While the anamorphic image may be captured using the refractive lens ofFIG. 1 or reflective lens of FIG. 7, the anamorphic image may also bederived from non-anamorphic images (e.g., a two-dimensional orthree-dimensional image), as will be described with more reference toFIGS. 12 through 15.

FIG. 12A graphically represents converting images captured without usingthe refractive lens of FIG. 1 or reflective lens of FIG. 7 (e.g., animage captured using a traditional camera) to a format suitable forviewing on the viewing surface PSH of FIG. 10A. In other words, FIG. 12Agraphically represents converting X_(O),Y_(O),Z_(O) coordinates toX_(VP), Z_(VP) coordinates (see FIG. 11) as viewed from the camera pointCP1. This format can then be displayed as described with reference toFIGS. 10A, 16, 17, and 18.

FIG. 12B is a flowchart illustrating a method 1200 of converting imagescaptured without using the refractive lens of FIG. 1 or reflective lensof FIG. 7 (e.g., an image captured using a traditional camera) to aformat suitable for viewing on the display of FIG. 10, according to oneembodiment. Thus, the method 1200 can be used to convert athree-dimensional point in space (e.g., the object point OP havingcoordinates X_(O),Y_(O),Z_(O)) to a point located on the viewing planeVP1 (e.g., a point having coordinates X_(VP), Z_(VP)). At step 1205, aline is extended between the object point OP having coordinatesX_(O),Y_(O),Z_(O) and the station point SP having coordinatesX_(SP),Y_(SP),Z_(SP). At step 1210, the coordinates of a point on theviewing surface PSH or picture plane PP having coordinatesX_(PP),Y_(PP),Z_(PP) defined by an intersection of the line extendingbetween the object point OP and the station point SP and the viewingsurface PSH are determined. At step 1215, a line is extended between thecamera point CP1 having coordinates X_(OP),Y_(OP),Z_(OP) and the pointon the viewing surface PSH having coordinates X_(PP),Y_(PP),Z_(PP). Atstep 1220, the coordinates of a point on the viewing plane VP1 or camerascreen CS having coordinates X_(VP), Z_(VP) defined by an intersectionof the line extending between the camera point CP1 and the point on theviewing surface PSH are determined.

According to one embodiment, Equation 28 through Equation 78, can beused to convert X_(O),Y_(O),Z_(O) coordinates to X_(VP), Z_(VP)coordinates as viewed from the camera point CP1, to be projected on animmersion vision display screen. As shown in FIG. 12A, a base point BPhaving a radius BR and coordinates X_(B),Y_(B),Z_(B) lies directly belowthe apex of the picture plane PP. Equation 28 through Equation 78 assumethat the base point BP has coordinates 0,0,0 and that the viewer islocated at the station point SP. The object point OP having coordinatesX_(O),Y_(O),Z_(O) or X_(OP),Y_(OP),Z_(OP) is located outside the viewingsurface PSH or picture plane PP with reference to the base point BP. Thelocation of the point on the picture plane PP having coordinatesX_(PP),Y_(PP),Z_(PP) can be determined on a vertical plane defined bythe object point OP and station point SP. Because the picture plane PPis symmetric about the Y-axis, the point on the picture plane PP havingcoordinates X_(PP),Y_(PP),Z_(PP) can be rotated about the Y-axis todefine all points on the picture plane PP in the vertical plane definedby the object point OP and station point SP.

Initially, an equation for the line defining the picture plane PP isdetermined. The origin ray angle ORA, which is the angle from horizontalof the origin ray OR, as measured about the point X_(PP),Y_(PP),Z_(PP)is determined from Equation 28 and Equation 29.

$\begin{matrix}{{O\; R\; A} = {{ATan}\left( \frac{\Delta \; Y}{\Delta \; X} \right)}} & {{Equation}\mspace{14mu} 28} \\{{O\; R\; A} = {{ATan}\left( \frac{\; {Y_{sp} - Y_{op}}}{X_{op} - X_{sp}} \right)}} & {{Equation}\mspace{14mu} 29}\end{matrix}$

A reflective ray angle RRA, where the reflective ray angle RRA is theangle from vertical of the reflective ray RR as measured about the pointX_(PP),Y_(PP),Z_(PP), can be determined given the locations of thestation point SP having coordinates X_(SP),Y_(SP),Z_(SP) and the camerapoint CP having coordinates X_(CP),Y_(CP),Z_(CP) from Equation 30 andEquation 31.

$\begin{matrix}{{R\; R\; A} = {{ATan}\left( \frac{\Delta \; Y}{\Delta \; X} \right)}} & {{Equation}\mspace{14mu} 30} \\{{R\; R\; A} = {{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)}} & {{Equation}\mspace{14mu} 31}\end{matrix}$

A mirrored angle MA, where the mirrored angle MA is the angle of theorigin ray OR to the reflective ray RR measured about the intersectionpoint of the origin ray OR to the viewing surface PSH as measured aboutthe point X_(PP),Y_(PP),Z_(PP), can be determined from Equation 32.

MA=90°+RRA−ORA   Equation 32

The origin to normal angle ONA, where the origin to normal angle ONA isthe angle from the origin ray OR to the normal line NL (to the pictureplane PP at intersection point X_(PP),Y_(PP),Z_(PP)) as measured aboutthe point X_(PP),Y_(PP),Z_(PP) can be determined from Equation 33.

$\begin{matrix}{{O\; N\; A} = \frac{MA}{2}} & {{Equation}\mspace{14mu} 33}\end{matrix}$

A normal angle NA, where the normal angle NA is the angle from thenormal line (N) to the horizontal can be determined from Equation 34.

NA=ONA−ORA   Equation 34

A tangent angle TA, where the tangent angle TA is the angle measuredfrom horizontal to the tangent line at the viewing surface PSH asmeasured about the point X_(PP),Y_(PP),Z_(PP) can be determined fromEquation 35.

TA=90°−NA   Equation 35

Combining the Equations:

$\begin{matrix}{{T\; A} = {{90{^\circ}} - \left( {{O\; N\; A} - {O\; R\; A}} \right)}} & {{Equation}\mspace{14mu} 36} \\{{T\; A} = {{90{^\circ}} - \left( {\frac{MA}{2} - {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}} \right)}} & {{Equation}\mspace{14mu} 37} \\{{T\; A} = {{90{^\circ}} - \left( {\frac{{90{^\circ}} + {RRA} - {O\; R\; A}}{2} - {A\; {{Tan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} \right)}} & {{Equation}\mspace{14mu} 38}\end{matrix}$

Simplifying the Equations:

$\begin{matrix}{{T\; A} = {{90{^\circ}} - \left( {\frac{90{^\circ}}{2} + \frac{RRA}{2} - \frac{O\; R\; A}{2} - {{A{Tan}}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}} \right)}} & {{Equation}\mspace{14mu} 39} \\{{T\; A} = {{90{^\circ}} - \frac{90{^\circ}}{2} - \frac{RRA}{2} + \frac{O\; R\; A}{2} + {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} & {{Equation}\mspace{14mu} 40}\end{matrix}$

Combining the Equations:

$\begin{matrix}{{T\; A} = {{90{^\circ}} - \frac{90{^\circ}}{2} - \frac{{ATan}\left( \frac{{X_{p}p} - X_{cp}}{Y_{pp} - Y_{cp}} \right)}{2} + \frac{{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - {X_{s}p}} \right)}{2} + {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} & {{Equation}\mspace{14mu} 41} \\{{T\; A} = {\frac{90{^\circ}}{2} - \frac{{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)}{2} + \frac{3 \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}{2}}} & {{Equation}\mspace{14mu} 42} \\{{T\; A} = \frac{{90{^\circ}} - {{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)} + {3 \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}}{2}} & {{Equation}\mspace{14mu} 43}\end{matrix}$

Equation 44 and Equation 45 can be used to determine an Equation of aline tangent to the viewing surface PSH at point X_(PP),Y_(PP),Z_(PP) inan elevation view (e.g., X and Y coordinates only), along the verticalplane defined by the station point and the object point.

Y=MX+b   Equation 44

Ypp=Tan(TA)×Xpp+b   Equation 45

Where b is the vertical offset between the base point BP of the dome tothe origin point OP of the coordinate system (e.g., assuming that thebase point BP and origin point OP of the coordinate system are thesame).

Combining the Equations:

$\begin{matrix}{Y_{pp} = {{{{Tan}\left( \frac{{90{^\circ}} - {{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)} + {3 \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}}{2} \right)} \times X_{pp}} + 0}} & {{Equation}\mspace{14mu} 46}\end{matrix}$

Simplifying the Equations:

$\begin{matrix}{Y_{pp} = {{{Tan}\left( {{45{^\circ}} - {\frac{1}{2}{{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)}} + {\frac{3}{2} \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} \right)} \times X_{pp}}} & {{Equation}\mspace{14mu} 47}\end{matrix}$

The Equation for a line from the station point SP to the object point OPcan be determined by calculating a horizontal length H of the line fromthe station point SP to the object point OP using Equation 48.

H=√{square root over (ΔX² +ΔY ²)}  Equation 48

Combining the Equations:

H=√{square root over ((X _(op) −X _(sp))²+(Z _(op) −Z_(sp))²)}  Equation 49

The vertical difference between the station point SP and the objectpoint OP can be determined from Equation 50.

ΔY=Y _(op) −Y _(sp)   Equation 50

The slope SL of the line between the station point SP and the objectpoint OP can be determined from Equation 51 and Equation 52.

$\begin{matrix}{{S\; L} = \frac{\Delta \; Y}{\Delta \; X}} & {{Equation}\mspace{14mu} 51} \\{{S\; L} = \frac{Y_{op} - Y_{sp}}{H}} & {{Equation}\mspace{14mu} 52}\end{matrix}$

Combining the Equations:

$\begin{matrix}{{S\; L} = \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}}} & {{Equation}\mspace{14mu} 53}\end{matrix}$

The Equation for the line from the station point SP to the object pointOP can be determined from Equation 54 and Equation 55.

Y=MX+b   Equation 54

Y _(pp) =SL×X _(pp) +b   Equation 55

where b is the vertical offset between the base point BP of the viewingsurface PSH to the origin point OP of the coordinate system (e.g.,assuming that the base point BP and origin point OP of the coordinatesystem are the same).

Combining the Equations:

$\begin{matrix}{Y_{pp} = {{\frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}} \times X_{pp}} + 0}} & {{Equation}\mspace{14mu} 56} \\{Y_{pp} = {X_{pp} \times \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}}}} & {{Equation}\mspace{14mu} 57}\end{matrix}$

To determine where the equations for the line of the picture plane PPand the line from the object point OP and the station point SPintersect, combine and simplify the Equations:

$\begin{matrix}{Y_{pp} = Y_{pp}} & {{Equation}\mspace{14mu} 58} \\{{{Tan}\; \left( {{45{^\circ}} - {\frac{1}{2}{{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)}} + {\frac{3}{2} \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} \right) \times X_{pp}} = {X_{pp} \times \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}}}} & {{Equation}\mspace{14mu} 59} \\{{{Tan}\left( {{45{^\circ}} - {\frac{1}{2}{{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)}} + {\frac{3}{2} \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} \right)} = \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}}} & {{Equation}\mspace{14mu} 60} \\{{{45{^\circ}} - {\frac{1}{2}{{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)}} + {\frac{3}{2} \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} = {{ATan}\left( \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}} \right)}} & {{Equation}\mspace{14mu} 61} \\{{{\frac{1}{2}{{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)}} + {\frac{3}{2} \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} = {{{ATan}\left( \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}} \right)} - {45{^\circ}}}} & {{Equation}\mspace{14mu} 62} \\{{{\frac{1}{2}{{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)}} + {\frac{3}{2} \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} = {{{ATan}\left( \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}} \right)} - {45{^\circ}}}} & {{Equation}\mspace{14mu} 63} \\{{{{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)} + {3 \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} = {{2 \times {{ATan}\left( \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}} \right)}} - {90{^\circ}}}} & {{Equation}\mspace{14mu} 64} \\{{{ATan}\left( \frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} \right)} = {{2 \times {{ATan}\left( \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}} \right)}} - {90{^\circ}} - {3 \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}}} & {{Equation}\mspace{14mu} 65} \\{\frac{X_{pp} - X_{cp}}{Y_{pp} - Y_{cp}} = {{Tan}\left( {{2 \times {{ATan}\left( \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}} \right)}} - {90{^\circ}} - {3 \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} \right)}} & {{Equation}\mspace{14mu} 66} \\{{X_{pp} - X_{cp}} = {\left( {Y_{pp} - Y_{cp}} \right) \times {{Tan}\left( {{2 \times {{ATan}\left( \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}} \right)}} - {90{^\circ}} - {3 \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} \right)}}} & {{Equation}\mspace{14mu} 67} \\{X_{pp} = {{\left( {Y_{pp} - Y_{cp}} \right) \times {{Tan}\left( {{2 \times {{ATan}\left( \frac{Y_{op} - Y_{sp}}{\sqrt{\left( {X_{op} - X_{sp}} \right)^{2} + \left( {Z_{op} - Z_{sp}} \right)^{2}}} \right)}} - {90{^\circ}} - {3 \times {{ATan}\left( \frac{Y_{sp} - Y_{op}}{X_{op} - X_{sp}} \right)}}} \right)}} + X_{cp}}} & {{Equation}\mspace{14mu} 68}\end{matrix}$

Next a line can be extended from intersection point on the picture planePP as viewed from above. When looking down at the X-Z plane, thedirectional angle DA, measured from the X-axis around the Y-axis, can bedetermined from Equation 69 and Equation 70.

$\begin{matrix}{{D\; A} = {{ATan}\; \frac{\Delta \; Z}{\Delta \; X}}} & {{Equation}\mspace{14mu} 69} \\{{D\; A} = {{ATan}\frac{Z_{op} - Z_{sp}}{X_{op} - X_{sp}}}} & {{Equation}\mspace{14mu} 70}\end{matrix}$

The horizontal length R of the previously determined line from thestation point SP to the picture plane PP can be determined from Equation71.

R=X_(pp)   Equation 71

The plot on the viewing plane VP1 can be determined Equation 72,Equation 73, and Equation 74 using the directional angle DA and radius Rfrom the center of the camera screen SC to the plot of X_(VP), Z_(VP).

$\begin{matrix}{\frac{X_{vp}}{R} = {{Cos}\mspace{11mu} \left( {D\; A} \right)}} & {{Equation}\mspace{14mu} 72} \\{X_{vp} = {R \times {Cos}\mspace{11mu} \left( {D\; A} \right)}} & {{Equation}\mspace{14mu} 73} \\{Z_{vp} = {R \times {Sin}\mspace{11mu} \left( {D\; A} \right)}} & {{Equation}\mspace{14mu} 74}\end{matrix}$

Combining and simplifying the Equations:

$\begin{matrix}{X_{vp} = {X_{pp} \times {Cos}\mspace{11mu} \left( {{ATan}\frac{Z_{op} - Z_{sp}}{X_{op} - X_{sp}}} \right)}} & {{Equation}\mspace{14mu} 75} \\{{Xvp} = \left\lbrack {\left( {{Ypp} - {Ycp}} \right) \times {\quad{{Tan}\left. \quad{\left( {{2 \times {{ATan}\left( \frac{{Yop} - {Ysp}}{\sqrt{\left( {{Xop} - {Xsp}} \right)^{2} + \left( {{Zop} - {Zsp}} \right)^{2}}} \right)}} - {90{^\circ}} - {3 \times {{ATan}\left( \frac{{Ysp} - {Yop}}{{Xop} - {Xsp}} \right)}}} \right) + {Xcp}} \right\rbrack \times {Cos}\mspace{11mu} \left( {{ATan}\frac{{Zop} - {Zsp}}{{Xop} - {Xsp}}} \right)}}} \right.} & {{Equation}\mspace{14mu} 76} \\{Z_{vp} = {X_{pp} \times {Sin}\mspace{11mu} \left( {{ATan}\frac{Z_{op} - Z_{sp}}{X_{op} - X_{sp}}} \right)}} & {{Equation}\mspace{14mu} 77} \\{{Zvp} = {\left\lbrack {{\left( {{Ypp} - {Ycp}} \right) \times {{Tan}\left( {{2 \times {{ATan}\left( \frac{{Yop} - {Ysp}}{\sqrt{\left( {{Xop} - {Xsp}} \right)^{2} + \left( {{Zop} - {Zsp}} \right)^{2}}} \right)}} - {90{^\circ}} - {3 \times {{ATan}\left( \frac{{Ysp} - {Yop}}{{Xop} - {Xsp}} \right)}}} \right)}} + {Xcp}} \right\rbrack \times {Sin}\mspace{11mu} \left( {{ATan}\frac{{Zop} - {Zsp}}{{Xop} - {Xsp}}} \right)}} & {{Equation}\mspace{14mu} 78}\end{matrix}$

FIG. 13 is a graphical illustration of converting an image capturedusing a traditional camera (e.g., movie or television images) to aformat suitable for viewing on the immersion vision screen usingEquation 28 through Equation 78, according to one embodiment. Forexample, a rectangular flat plane can be defined in a three-dimensionalimmersive environment and the X-Y coordinates of the plane, as well asthe color and intensity characteristics of the image or movie, can beassigned to correlating points on the flat plane with a sufficientnumber of points to achieve the desired image resolution. Each of thepoints defined on the plane in immersive space is then plotted to theviewing plane VP1 in a manner similar to that described with referenceto FIGS. 12A and 12B. Thus, when the anamorphic image of the movie orstill image is displayed on the viewing surface PSH, the viewerperceives a two-dimensional rectangular image as viewed from the stationpoint SP.

FIG. 14 is a graphical illustration of converting a computer graphicsimage, such as a traditional graphical user interface object to a formatsuitable for viewing on the immersion vision screen using Equation 28through Equation 78, according to one embodiment. In a manner similar tothat described with reference to FIGS. 12A and 12B, three-dimensionalconstructs depicting program icons, folders, files and program windowsare defined and then the parts of the construct visible from the stationpoint SP are plotted to the viewing surface PSH and then to the viewingplane VP1. For example, the window or icon of a piece of software may beconverted so that the immersion vision screen can be used as an expandeddesktop (e.g., the windows float about the user). When used to displaywebsites, the immersion vision system helps create three-dimensionalpanoramic environments that bring a new level of interaction and depthof detail to the internet experience.

FIG. 15 is a graphical illustration of converting an image suitable forviewing on the immersion vision screen to a format suitable for printingas a photograph having a traditional aspect ratio using Equation 28through Equation 78, according to one embodiment. For example, the usermay select a partial image from within the immersion vision panoramicformat (e.g., by highlighting or framing a desired image as seen by theviewer located at the station point SP) so that the desired image can beprinted as a flat rectangular photograph.

In order to select an area of the image displayed around the viewer todefine the area for printing, a rectangle within the field of view asobserved from the station point SP is defined. The following exampleprovides a mathematical analysis of the various image manipulations.This example assumes that the viewer is viewing the image from thestation point SP inside the lens of FIG. 7 on the reflective surface asthey would view the image on the Harris shaped display surface at anormal scale. For this example, the distance between the base point BPand the furthest extent of the surface PSH is approximately threeinches. The distance from the base point BP of the refractive lens tothe camera point CP1 is approximately nine inches. The angle from thehorizon line to the edge of the field of view of the lens is 30 degrees,which makes the distance from the base point BP to the station point SPapproximately 1.7321 inches. The center point of the coordinate system(0,0) is located at the station point SP. The center point of therectangle is located on a sphere having a radius of approximately fourinches from the station point SP. For the purpose of simplicity thedirection of viewing is along the direction of the z-axis and level withthe horizon line and the selection rectangle is located within the x-yplane.

All rectangles have a center point of the rectangle located on thesurface of an imaginary sphere of a fixed radius about the station pointSP where this fixed radius is outside the exterior surface of thereflective lens, and the rectangle is perpendicular to the line from thestation point SP to the center point of the rectangle.

With reference to FIG. 13, the viewer at the station point SP perceivesa rectangle framing a portion of the anamorphic image projected on theviewing screen surface PSH. The rectangle is defined as threedimensional points having coordinates defining the center point and thefour corners of the selection rectangle. In this example, the centerpoint is located at coordinates (4,0,0). If the selection rectangle istwo inches wide (in the x-direction) and 1.6 inches tall (in they-direction), the four corners of the selection rectangle are located atcoordinates (−1,0.8,0), (1,0.8,0), (1,−0.8,0) and (−1,−0.8,0). The sizeand shape of the selection rectangle can be varied by adjusting thecoordinate values of the corners of the selection rectangle.

With reference to FIG. 12 and Equation 68, the coordinates of thecorners of the selection rectangle as displayed on the viewing plane VP1can be determined by solving Equation 68 for the surface of therectangle. For example, entering the hypothetical data (e.g.,Y_(cp)=7.268; Y_(sp)=X_(sp)=Z_(sp)=X_(cp)=0; X_(op), Y_(op), and Z_(op)varies for each point) into Equation 68 yields the X_(pp) coordinate forthe center point of the selection rectangle as well as the X_(pp)coordinates of the four corners of the selection rectangle plotted tothe surface PSH, as shown in Equation 79.

$\begin{matrix}{X_{pp} = {{\left( {Y_{pp} - 7.268} \right) \times {{Tan}\left( {{2 \times {{ATan}\left( \frac{Y_{op} - 0}{\sqrt{\left( {X_{op} - 0} \right)^{2} + \left( {Z_{op} - 0} \right)^{2}}} \right)}} - {90{^\circ}} - {3 \times {{ATan}\left( \frac{0 - Y_{op}}{X_{op} - 0} \right)}}} \right)}} + 0}} & {{Equation}\mspace{14mu} 79}\end{matrix}$

The object points for the selection rectangle (X_(op), Y_(op), Z_(op))can be set for this example so that the center point has coordinates(4,0,0) and the corner points have coordinates (−1,0.8,0), (1,0.8,0),(1,−0.8,0) and (−1,−0.8,0). Because the variable X_(pp) in Equation 79is the same variable as X_(PSH) shown in Equation 80, Equation 79 can becombined with Equation 16 to yield Equation 80 which states the value ofY_(pp) as a function of the known object point values (X_(op), Y_(op),Z_(op)) for the selection rectangle in this example.

$\begin{matrix}{{Xpp} = {\left( {{Ypp} - 7.268} \right) \times {{Tan}\left( {{2 \times {{ATan}\left( \frac{0}{\sqrt{(4)_{2} + (0)_{2}}} \right)}} - {90{^\circ}} - {3 \times {{ATan}\left( \frac{- 0}{4} \right)}}} \right)}}} & {{Equation}\mspace{14mu} 80}\end{matrix}$

Equation 80 uses the center point of the selection rectangle as anexample of calculating the X_(pp) coordinate from the coordinates of theobject points using Equation 16. In this example, the X_(pp) value ofthe center point of the selection rectangle can be determined fromEquation 16 to be X_(pp)=22. Then, Equation 80 can be used with the datafor the object point coordinates of each of the respective four cornersof the selection rectangle to calculate the X_(pp) for each of thecorners.

Next, a resolution may be defined by selecting the number of pixels inthe rectangle. Then image characteristics may be assigned to the pixelsin the rectangle. In addition, the color and intensity characteristicsof the image or movie can be assigned to correlating points on the flatplane with a sufficient number of points to achieve the desired imageresolution. An image file of pixels of the rectangle can then be storedand printed.

Thus, a digital camera or movie camera using the refractive lens of FIG.1 or reflective lens of FIG. 7 makes the vision station an ideal setupfor viewing photos and editing the immersion vision images in apanoramic format.

Display

Referring now to FIG. 10A, a display according to one embodiment usesthe Harris shape for the viewing surface PSH. A projector may be locatedat point CP and project an image on the viewing surface PSH. The usermay then view the image from the station point SP located on the otherside of the viewing surface PSH. Alternatively, the viewing surface PSHmay be a volatile flat panel display, such as a liquid crystal display(LCD), organic light-emitting diode display (OLED), or light-emittingdiode display (LED), or a static flat panel display, such as a polymerstabilized cholesteric liquid crystal display, taking a Harris shape.This may require an algorithm that converts the photo captured using thereflective/refractive lens above to the addressed display. According toanother embodiment, the outside surface of the shell is lined with imagecapture devices that can communicate with the display on the innersurface of the shell. This may allow a projector to be used and may helpcontrol the amount of light incident the user's retina.

FIG. 10B is a cross-section of the viewing surface PSH shown in FIG.10A. As shown in FIG. 10B, the viewing or station point SP is located onthe concave side of the viewing surface PSH and the focal or camerapoint CP1 is located on the convex side of the viewing surface PSH.According to one embodiment, the viewing surface PSH takes the sameshape as the reflective surface PSH described with reference to the lensof FIG. 7. Thus, if the viewing surface PSH was reflective, all lightrays passing through the viewing surface PSH and directed toward theviewing point SP would reflect off the viewing surface PSH and intersectat the focal point CP1. In other words, if the viewing surface PSH wasreflective, any two rays (e.g., rays R_(1SP) through R_(5SP)) passingthrough the viewing surface PSH toward the viewing point SP separated bya viewing angle β would reflect off the viewing surface PSH andintersect at the focal point CP1 separated by an angle α, and the angleα would be the same regardless of direction from which the two raysseparated by the viewing angle β originate. The viewing surface PSH mayinclude a set of points defined by the intersections of rays R_(1SP)through R_(5SP) emanating from the viewing point SP and correspondingrays R_(1CP) through R_(5CP) emanating from the focal point CP1. Whileonly ten rays are show in FIG. 10B, it should be recognized that theviewing surface PSH may include a set of points defined by theintersections of more than ten rays. The rays R_(1CP) through R_(5CP)are separated by angles α₁ through α₄, where α₁=α₂=α₃=α₄. Likewise, therays R_(1SP) through R_(5SP) are separated by angles β₁ through β₄,where β₁=β₂=β₃=β₄. The angles α and β do not need to be equal. Accordingto one embodiment, β₁ through β₄ together define the field of view ofthe viewing surface PSH and add to approximately 240 degrees (e.g., β₁and β₂ add to approximately 120 zenith degrees and β₃ and β₄ add toapproximately 120 zenith degrees).

The displays or immersion vision screens can take may sizes. For examplea work station display (FIG. 16) may be suitable for one or two viewers,a home theatre display (FIG. 17) may be suitable for a small group ofviewers, and a movie theatre display (FIG. 18) may be suitable for alarge group of viewers.

With reference to FIG. 16, the work station display may be used as anindividual computer display or display workstation. According to oneembodiment, the entire structure measures approximately 7 feet by 7 feeton the floor and measures approximately 7 feet 11 inches high. Theviewing screen size may be approximately 6 feet in diameter with ascreen height of approximately 2 feet 8 inches. The screen can pivotupward and may be counter-balanced to open and close with ease. Theprojector may be mounted overhead and can be reflected off a flat mirrordownward onto a translucent acrylic shell used as a viewing surface.

The vision station viewing surface or projection screen may be made witha thermo-pneumatically molded clear acrylic sheet. The exterior surfaceof the screen may then be etched to prepare the surface to receive theprojected image. The supporting structure for the screen and projectormay be made with welded tube steel covered with sheet metal and woodveneers. In addition, the supporting structure may include pneumaticformwork. The computer may be of standard manufacture with a high levelof graphics speed and capability. The projector may be a standarddigital projector of high resolution.

Referring now to FIG. 17, the home theatre display (vision room) isshown that may be used as an entertainment theatre room or as aconference room. The vision room viewing screen may utilize a Harrisshape and may be designed for use by three or eight people. Accordingly,the viewing screen size may be, for example, 7 feet to 20 feet indiameter with a screen height ranging from 3 feet to 9 feet. However,other sizes may be used based on the application. The projector may beoverhead and project downward onto an acrylic shell used as a viewingsurface.

The vision room viewing surface or projection screen may be made withthermo-pneumatically molded clear acrylic sheets. The exterior surfaceof the screen may then be etched to prepare the surface to receive theprojected image. The supporting structure for the screen and projectormay be made with welded tube steel covered with sheet metal and wood.The entire screen, projector and computer may be contained within a homeor business which may be darkened for better viewing.

FIG. 18 shows the movie theatre display (vision theatre) being used amovie or entertainment theatre. The vision theatre viewing screen mayutilize a Harris shape. It may be designed for use by 25 to 50 people.Accordingly, the viewing screen size may be 16 feet in diameter with ascreen height of approximately 9 feet. However, other sizes may be usedbased on the application. The projector may be overhead and projectdownward onto an acrylic shell used as a viewing surface.

Referring now to FIG. 19, a camera is shown utilizing the refractivelens of FIG. 1. The camera is shown installed on a tripod mount TPM, andmay include a leveling indicator, a remote control for hands free cameraoperation, a camera body having a display screen, lights, microphones,power supply connection and a battery cover. FIG. 20 is a block diagramshowing operational components of an example camera 10. The camera 10includes a processor 20, which may be any commercially availableprocessor or other logic machine capable of executing instructions. Animage capture device 30 is communicatively coupled to the processor 20via a bus 40. A lens 50 (e.g., the refractive lens described withreference to FIG. 1) is provided to focus light on the image capturedevice 30. The image capture device 30 may comprise a wide range ofimage sensing devices for converting an optical image (or another wavein the electromagnetic spectrum) into an electrical signal. For example,the image capture device 30 may comprise a charged coupled device (CCD)sensor or complimentary metal oxide semiconductor (CMOS) sensor operableover the visible spectrum. However, the image capture device 30 may takeanother form and may be operable over other spectrums, such as theinfrared spectrum. As previously discussed, the image capture device 30may also comprise photographic film, film stock, or another devicecapable of capturing an optical image.

The camera 10 presents data, photographs, menus, prompts, and otherwisecommunicates with the user via one or more display devices 60, such as atransmissive or reflective liquid crystal display (LCD), organiclight-emitting diode (OLED), cathode ray tube (CRT) display, or othersuitable micro display. A display controller 62 drives display device 60and is coupled to bus 40.

The camera 10 may include a standard input controller 70 to receive userinput from one or more buttons 80, a pointing device (not shown), orother wired/wireless input devices. Other input devices may include amicrophone, touchscreen, touchpad, trackball, or the like. While theinput devices may be integrated into the camera 10 and coupled to theprocessor 20 via the input controller 70, the input devices may alsoconnect via other interfaces, such as a connector 90. The connector 90may include one or more data interfaces, bus interfaces, wired orwireless network adapters, or modems for transmitting and receivingdata. Accordingly, the input controller 70 may include hardware,software, and/or firmware to implement one or more protocols, such asstacked protocols along with corresponding layers. Thus, the connector90 may function as a serial port (e.g., RS232), a Universal Serial Bus(USB) port, and/or an IR interface. The input controller 80 may alsosupport various wired, wireless, optical, and other communicationstandards.

A network interface 100 may be provided to communicate with an externalnetwork, a computer, or another camera. The network interface 100 mayfacilitate wired or wireless communication with other devices over ashort distance (e.g., Bluetooth™) or nearly unlimited distances (e.g.,the Internet). In the case of a wired connection, a data bus may beprovided using any protocol, such as IEEE 802.3 (Ethernet), AdvancedTechnology Attachment (ATA), Personal Computer Memory Card InternationalAssociation (PCMCIA), and/or USB, for example. A wireless connection mayuse low or high powered electromagnetic waves to transmit data using anywireless protocol, such as Bluetooth™, IEEE 802.11b (or other WiFistandards), Infrared Data Association (IrDa), and/or Radio FrequencyIdentification (RFID), for example.

The camera 10 may include a memory 110, which may be implemented usingone or more standard memory devices. The memory devices may include, forinstance, RAM 112, ROM 114, and/or EEPROM devices, and may also includemagnetic and/or optical storage devices, such as hard disk drives,CD-ROM drives, and DVD-ROM drives. The camera 10 may also include aninterface 120 coupled to an internal hard disk drive 130. The interface120 may also be coupled to a removable memory 140, such as flash memory.In addition, the interface 120 may also be coupled to a magnetic floppydisk drive (not shown), an optical disk drive (not shown), or anotherdrive and may be configured for external drive implementations, such asover a USB, IEEE 1194, or PCMCIA connection. Thus, the memory 140 may bephysically removable from the camera 10 or data stored in the memory 140may be accessed using a wired or wireless connection.

In one embodiment, any number of program modules are stored in thedrives (e.g., drive 130) and ROM 114, including an operating system (OS)150, one or more application programs 152 (e.g., image compressionsoftware), other program modules 154, and data 156. All or portions ofthe program modules may also be cached in RAM 112. Any suitableoperating system 150 may be employed.

The camera 10 may include a battery 160 and a battery interface 162 forinterfacing with battery 160, such as for charging battery 160 ordetecting a charge level of battery 160. The battery 160 can be anyelectrical or electrochemical device, such as galvanic cells or fuelcells, and can be rechargeable or non-rechargeable. The battery 160 maybe located inside of the camera 10 or attached to the outside of thecamera 10. In the case of non-rechargeable batteries, the battery 160may be physically detachable or removable from the camera 10. In thecase of rechargeable batteries, the battery 160 may be recharged in anynumber of ways. For example, the battery 160 may be physicallydetachable or removable from the camera 10 to allow charging by anexternal battery charger (not shown). In addition, an access port 164may be provided to provide a connection for an external battery charger.

As previously described, image data captured using the camera 10 can betransferred (e.g., using a wired or wireless connection or by removingthe removable memory 140) to a computer for display on one or more ofthe previously described displays. FIG. 21 is a block diagram showingoperational components of an example computer 200. The computer 200includes a processor 210, which may be any commercially availableprocessor or other logic machine capable of executing instructions. Adisplay controller 220 is coupled to bus 230 and drives one or moredisplay devices 240. The display device(s) 240 may comprise any of thedisplay previously described with reference to FIGS. 10A, 11, and 16-18,or another display device suitable to presents data, photographs, menus,prompts, and otherwise communicates with the user.

The computer 200 may include a standard input controller 250 to receiveuser input from an input put device such as a pointing device or otherwired/wireless input devices. Other input devices may include amicrophone, touchscreen, touchpad, trackball, or the like. While theinput devices may be integrated into the computer 200 and coupled to theprocessor 210 via the input controller 250, the input devices may alsoconnect via other interfaces, such as a connector 260. The connector 260may include one or more data interfaces, bus interfaces, wired orwireless network adapters, or modems for transmitting and receivingdata. Accordingly, the input controller 250 may include hardware,software, and/or firmware to implement one or more protocols, such asstacked protocols along with corresponding layers. Thus, the connector260 may function as a serial port (e.g., RS232), a Universal Serial Bus(USB) port, and/or an IR interface. The input controller 260 may alsosupport various wired, wireless, optical, and other communicationstandards. In addition, a printer controller 254 is provided tointerface with a printer 256 (e.g., via a bi-direction port, such as aIEEE 1284 parallel port, or a wired or wireless network connection).

A network interface 270 may be provided to communicate with an externalnetwork, another computer, or a camera. The network interface 270 mayfacilitate wired or wireless communication with other devices over ashort distance (e.g., Bluetooth™) or nearly unlimited distances (e.g.,the Internet). In the case of a wired connection, a data bus may beprovided using any protocol, such as IEEE 802.3 (Ethernet), AdvancedTechnology Attachment (ATA), Personal Computer Memory Card InternationalAssociation (PCMCIA), and/or USB, for example. A wireless connection mayuse low or high powered electromagnetic waves to transmit data using anywireless protocol, such as Bluetooth™, IEEE 802.11b (or other WiFistandards), Infrared Data Association (IrDa), and/or Radio FrequencyIdentification (RFID), for example.

The computer 200 may include a memory 280, which may be implementedusing one or more standard memory devices. The memory devices mayinclude, for instance, RAM 282, ROM 284, and/or EEPROM devices, and mayalso include magnetic and/or optical storage devices, such as hard diskdrives, CD-ROM drives, and DVD-ROM drives. The computer 200 may alsoinclude an interface 290 coupled to an internal hard disk drive 300. Inaddition, the interface 290 may also be coupled to a magnetic floppydisk drive (not shown), an optical disk drive (not shown), or anotherdrive and may be configured for external drive implementations, such asover a USB, IEEE 1194, or PCMCIA connection.

In one embodiment, any number of program modules are stored in thedrives (e.g., drive 300) and ROM 284, including an operating system (OS)310, one or more application programs 312 (e.g., image compressionsoftware), other program modules 314 (e.g., an image conversion moduleor any of the algorithms described with reference to FIGS. 13-15), anddata 316. All or portions of the program modules may also be cached inRAM 282. Any suitable operating system 310 may be employed.

The methods and systems described herein may be implemented in and/or byany suitable hardware, software, firmware, or combination thereof.Accordingly, as used herein, a component or module may comprisehardware, software, and/or firmware (e.g., self-contained hardware orsoftware components that interact with a larger system). A softwaremodule or component may include any type of computer instruction orcomputer executable code located within a memory device and/ortransmitted as electronic signals over a system bus or wired or wirelessnetwork. A software module or component may, for instance, comprise oneor more physical or logical blocks of computer instructions, which maybe organized as a routine, program, object, component, data structure,etc., that performs one or more tasks or implements particular abstractdata types.

In certain embodiments, a particular software module or component maycomprise disparate instructions stored in different locations of amemory device, which together implement the described functionality ofthe module. Indeed, a module may comprise a single instruction or manyinstructions, and may be distributed over several different codesegments, among different programs, and across several memory devices.Some embodiments may be practiced in a distributed computing environmentwhere tasks are performed by a remote processing device linked through acommunications network. In a distributed computing environment, softwaremodules may be located in local and/or remote memory storage devices. Inaddition, data being tied or rendered together in a database record maybe resident in the same memory device, or across several memory devices,and may be linked together in fields of a record in a database across anetwork.

Embodiments may include various steps, which may be embodied inmachine-executable instructions to be executed by processor 20,processor 210, or another processor. Alternatively, the steps may beperformed by hardware components that include specific logic forperforming the steps or by a combination of hardware, software, and/orfirmware. A result or output from any step, such as a confirmation thatthe step has or has not been completed or an output value from the step,may be stored, displayed, printed, and/or transmitted over a wired orwireless network. For example, a captured image may be stored,displayed, or transmitted over a network.

Embodiments may be provided as a computer program product including amachine-readable storage medium having stored thereon instructions (incompressed or uncompressed form) that may be used to program a computer(or other electronic device) to perform processes or methods describedherein. The machine-readable storage medium may include, but is notlimited to, hard drives, floppy diskettes, optical disks, CD-ROMs, DVDs,read-only memories (ROMs), random access memories (RAMs), EPROMs,EEPROMs, flash memory, magnetic or optical cards, solid-state memorydevices, or other types of media/machine-readable medium suitable forstoring electronic instructions. Further, embodiments may also beprovided as a computer program product including a machine-readablesignal (in compressed or uncompressed form). Examples ofmachine-readable signals, whether modulated using a carrier or not,include, but are not limited to, signals that a computer system ormachine hosting or running a computer program can be configured toaccess, including signals downloaded through the Internet or othernetworks. For example, distribution of software may be via CD-ROM or viaInternet download.

As previously discussed, the immersion vision system may be used for animmersive environment display of a standard computer operating systemresulting in a display of icons and program windows that surround theviewer (see, e.g., FIG. 14). Each rectangular icon or program windowappears to the viewer within the immersion vision screen as a rectanglewithin an immersive viewing environment through the manipulation of theflat, 2 dimensional image by one or more of the conversion algorithmspreviously discussed. Internet web sites can be visually immersive wherethe observer is within an environment.

Additionally, the immersion vision system may be used for imagegeneration and display of three-dimensional computer simulationenvironments, including flight simulation, military tactical display,gaming environments, internet web sites and architectural andengineering computer design programs through the manipulation of XYZCartesian coordinates by one or more of the conversion algorithmspreviously discussed to display the three-dimensional information on theimmersion vision viewing screen thereby immersing the viewer in thethree-dimensional environment. Software applications may include 3-Ddesign programs, 3-D internet websites, and 3-D simulation programs.

In one embodiment, the immersion vision system may be used as animproved security surveillance system where the viewer is surrounded bythe image of a remote location being monitored with a camera having animmersion vision lens. The viewer may have the advantage of seeing theentire area under surveillance at one time without panning the image.The immersive image allows the viewer to observe the interaction betweenindividuals physically separated within the area under observation, anobservation not possible with current security surveillance systems.

In another embodiment, the immersion vision system may be used for thedisplay of medical images such X-ray photographs, images generatedduring fluoroscopy, and images generated during magnetic resonanceimaging (MRI). The images may be manipulated using one or more of theconversion algorithms previously discussed to display thethree-dimensional information on the immersion vision viewing screen toimmerse the viewer in the three-dimensional environment. The scannedmedical data can be viewed as an image surrounding the viewer, where theviewer is perceiving the image as if they were small in scale andviewing the scanned data as if they are within the heart, lungs,stomach, vein or other structure of the body.

According to one embodiment, an immersion vision imaging system uses amathematically defined Harris shape to capture, create, and displaypanoramic images, the immersion vision system. The system may includelenses, image collection devices, viewing screens and softwarealgorithms, all based on a Harris shape, so that they may be used inconjunction to capture, create, and display panoramic pictures on asurface of a viewing screen that encloses a viewer (See, e.g., FIGS. 1and 10A).

For example, a reflective camera lens may gather immersion vision imageswhose outermost reflective shape of the lens is defined as a Harrisshape and consists of a surface that reflects all light headed to theviewing or station point SP to the camera point CP1 to capture panoramicimages for use in the immersion vision system (See, e.g., FIG. 8). Byway of another example, a refractive camera lens may gather immersionvision images and further comprise a series of refractive lenses tocapture panoramic images formatted for use in the immersion visionsystem (See, e.g., FIG. 1). The immersion vision refractive lens designmay utilize a Harris shape in the design of the lenses where the path oftravel of the light through the lens passes through an imaginary pictureplane IPP as it travels to the camera point CP, such that the image onthe viewing plane VP2 is the exact, or reverse of the image on theviewing plane VP1 using the immersion vision reflective lens given thatthe source of the image is the same.

One or more software algorithms may use a Harris shape equation tocomputer generate immersion vision images for display on an immersionvision viewing screen (See, e.g., FIG. 13). For example, amathematically defined Harris shape (See, e.g., FIG. 7) may be used in aAlgorithm for the conversion of three-dimensional image data points(using the Cartesian coordinate system defined in terms of X_(O), Y_(O),Z_(O)), to points (defined as X_(VP), Y_(VP)), for use on an immersionvision screen. Such an algorithm may be used in gaming andthree-dimensional software programs to generate visual output tovisually immerse the viewer in a panoramic image (see, e.g., FIG. 12A).

By way of another example, a software algorithm may use a Harris shapeequation to computer generate images for viewing on an immersion visionviewing screen by modifying the format of two-dimensional images,defined in an XY plane for viewing in the immersion vision system. Oneexample of this (X,Y) to (X_(VP),Y_(VP)) algorithm is illustrated inFIG. 13 which converts two-dimensional or flat plane images such asstill photographs, movie, television and computer images into a formatto be viewed in the immersion vision environment. This algorithm may usea Harris shape to mathematically translate the (X,Y) Cartesiancoordinates of a flat plane image, to points defined as (X_(VP),Y_(VP))for display on an immersion vision screen. This algorithm may be used toview a two-dimensional plane image as a flat plane with the imagelocated within a perceived three-dimensional environment.

One or more software algorithms using the Harris shape equation may beused to mathematically translate the X-Y Cartesian coordinates of a flatplane image, to points defined as (X_(VP),Y_(VP)) for display on animmersion vision screen. On example of this is the (X,Y) to(X_(VP),Y_(VP)) algorithm illustrated in FIG. 14 which allows the flatdesktop or background screen images to surround you on the immersionvision viewing screen. Additionally, operating system icons and softwareprogram windows may be displayed around the viewer. This algorithm maybe used to view the two-dimensional window images as two-dimensionalplanes located within a perceived three-dimensional environment.

One or more software algorithms may use a Harris shape equation tomathematically translate the X-Y Cartesian coordinates of a flat planeimage, to points defined as (X_(VP),Y_(VP)) for display on an immersionvision screen. One example of this is the (X_(VP),Y_(VP)) to (X,Y)algorithm illustrated in FIG. 15 which allows the images on theimmersion vision viewing screen surrounding the user to be selected andcropped for printing in a standard (X,Y) image format. This algorithmmay allow images to be captured in the immersion vision panoramic formatand then selections to be printed as standard flat photo images.

One or more viewing screens may be used for viewing panoramic images inthe shape defined as a Harris shape (See, e.g., FIG. 16). For example, aprojection viewing immersion vision screen may comprise a viewing screenthat employs projector technology, that is the source of light for imageviewing, to project the image on the exterior convex surface of theviewing screen to be viewed on the interior or concave surface of theviewing screen. Additionally, a direct viewing immersion vision screenmay comprise a viewing screen that employs technology, such as lightemitting diodes (LED), that generate the light for image viewing at thesurface of the viewing screen.

A shape of the vision station viewing screen may comprise a viewingscreen measuring approximately 6 feet across the base and approximately2 to 3 feet high used for one or two people to view images in theimmersion vision format. As illustrated in FIG. 16 the Vision Stationmay be an ideal panoramic viewing environment for personal computing,security imaging, surfing the internet, computer gaming, 3D CAD designplatform, and panoramic movie viewing.

A shape of the vision room viewing screen may comprise a viewing screenmeasuring approximately 7 to 20 feet across the base and approximately 3to 9 feet high used for a room of people to view images in the immersionvision format. As illustrated in FIG. 17 the Vision Room may be an idealpanoramic viewing environment for panoramic movie viewing. groupcomputing, computer gaming, and used for the viewing of any immersionvision images.

A shape of the vision theatre viewing screen may comprise a viewingscreen measuring approximately 21 to 50 feet across the base andapproximately 9 to 20 feet high used for a room of people to view imagesin the immersion vision format. As illustrated in FIG. 18 the visiontheatre may be an ideal panoramic viewing environment for panoramicmovie viewing. broadcast special events, classroom instruction, and maybe used for the viewing of any immersion vision images.

The terms and descriptions used herein are set forth by way ofillustration only and are not meant as limitations. Those skilled in theart will recognize that many variations can be made to the details ofthe above-described embodiments without departing from the underlyingprinciples of the invention.

The terms and descriptions used herein are set forth by way ofillustration only and are not meant as limitations. Those skilled in theart will recognize that many variations can be made to the details ofthe above-described embodiments without departing from the underlyingprinciples of the invention. The scope of the invention should thereforebe determined only by the following claims (and their equivalents) inwhich all terms are to be understood in their broadest reasonable senseunless otherwise indicated.

1-17. (canceled)
 18. A system for generating an anamorphic image from anon-anamorphic image, comprising: a memory for storing at least onedataset defining a non-anamorphic image; and a processor communicativelycoupled to the memory, the processor configured to: convert a datasetdefining a non-anamorphic image into at least one anamorphic imagesuitable for displaying on a viewing surface such that an image viewedon the viewing surface appears undistorted from a viewing point; andstore the at least one anamorphic image in the memory.
 19. A system asset forth in claim 18, wherein the non-anamorphic image comprises atwo-dimensional image.
 20. A system as set forth in claim 18, whereinthe non-anamorphic image comprises a three-dimensional image.
 21. Asystem as set forth in claim 18, further comprising: a shell sized to aleast partially surround a viewer, the shell having a convex exteriorsurface opposite a concave interior surface, the concave interiorsurface at least partially defining the viewing surface and at leastpartially defined with respect to the viewing point and a focal pointlocated on opposite sides of the viewing surface such that all lightrays passing through the viewing surface and directed toward the viewingpoint would reflect off the viewing surface and intersect at the focalpoint if the viewing surface was reflective; and a projectorcommunicatively coupled to the processor, wherein the shell and theprojector are configured such that the projector projects the anamorphicimage onto the convex exterior surface of the shell so that a viewer canview an image on the viewing surface that appears undistorted from apoint of view.
 22. A system as set forth in claim 18, furthercomprising: a display device sized to a least partially surround aviewer and having a concave interior surface at least partially definingthe viewing surface and at least partially defined with respect to theviewing point and a focal point located on opposite sides of the viewingsurface such that all light rays passing through the viewing surface anddirected toward the viewing point would reflect off the viewing surfaceand intersect at the focal point if the viewing surface was reflective,wherein the display device is communicatively coupled to the processorand the display device is configured to display the anamorphic imagesuch that a viewer can view an image on the viewing surface that appearsundistorted from a point of view.
 23. A system as set forth in claim 18,further comprising: a memory for storing at least one dataset definingan anamorphic image; a screen having a concave surface at leastpartially defining the viewing surface; an image source for displayingthe anamorphic image on the viewing surface such that an image viewed onthe viewing surface appears undistorted from a point of view; an inputdevice configured to select a portion of the anamorphic image; and aprocessor communicatively coupled to the memory, the input device, andthe image source, the processor configured to: convert the selectedportion of the anamorphic image into at least one non-anamorphic image;and store the at least one non-anamorphic image in the memory.
 24. Asystem as set forth in claim 18, further comprising: a printercommunicatively coupled to the processor, and wherein the processor isfurther configured to print the at least one non-anamorphic image.25-44. (canceled)